I believe I have gathered enough information that an answer is now available.
Three main variables determine the direction roots grow: Gravity, light, and water. These are called gravitropism, phototropism, and hydrotropism.
Phototropism is simply that the roots grow away from the light. I wouldn't think light extends much below the surface, so this tropism is minimal to none concerning grass.
From http://en.wikipedia.org/wiki/Hydrotropism
Hydrotropism is a plant's growth response in which the direction of growth is determined by a stimulus or gradient in water concentration. A common example is a plant root growing in humid air bending toward a higher relative humidity level. This is of biological significance as it helps to increase efficiency of the plant in its ecosystem. Hydrotropism is difficult to observe in underground roots, since the roots are not readily observable, and root gravitropism is usually more influential than root hydrotropism. Water readily moves in soil and soil water content is constantly changing so any gradients in soil moisture are not stable.
Misconceptions
The greater growth of roots in moist soil zones than in dry soil zones is not usually a result of hydrotropism. Hydrotropism requires a root to bend from a drier to a wetter soil zone. Roots require water to grow so roots that happen to be in moist soil will grow and branch much more than those in dry soil.
Roots cannot sense water inside intact pipes via hydrotropism and break the pipes to obtain the water.
Roots cannot sense water several feet away via hydrotropism and grow toward it. At best hydrotropism probably operates over distances of a couple millimeters.
From http://en.wikipedia.org/wiki/Gravitropism
Abundant evidence demonstrates that roots bend in response to gravity due to a regulated movement of the plant hormone auxin known as polar auxin transport (Swarup et al., 2005).
From http://udspace.udel.edu/bitstream/handle/19716/2830/Chapter%205.%20Roots%20and%20Root%20Systems.pdf
Root growth results from cell division and the pressure developed by enlargement
of newly formed cells. Cell enlargement is discussed in Chapter 11 and
root growth at the cellular level is discussed by Barlow in Gregory et at. (1987).
Bret-Harte and Silk (1994) question how sufficient carbon for growth reaches
root meristems, which are several millimeters beyond the termination of the
phloem. The older portions of roots are anchored in the soil and the tips are
pushed forward through the soil by cell enlargement at rates of a few millimeters
to a few centimeters daily, often following a tortuous path of least resistance
through crevices and around pebbles and other obstructions. Generally, root
tips tend to return to their original direction of growth after passing around
obstacles, a characteristic observed in the 19th century by Darwin and others,
which is known as exotropy (Wilson, 1967). Despite numerous temporary deflections,
branch roots of many plants tend to grow outward for a time before
turning downward (Wild, 1988, p. 121 and Fig. 5.11). The cause of this change
in sensitivity of roots to gravity deserves more study.
Therefore, the roots aren't growing down because of the presence of deep water, they're growing downward because of gravity and, being a healthy root, that's what roots do. If there is some hydrotropism involved, it certainly isn't necessary since the roots are already growing in the direction of gravity.
So to get deep roots, all we need is gravity and a healthy plant.
One caveat to this may be if hydrotropism could overpower gravitropism if somehow there is more water near the surface than deeper in the soil.
From: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1838587/
The classical methods of the German botanists, also used by the Darwins included placing seeds in a hanging cylinder of wet sawdust, which resulted in roots first growing downward (gravitropism) but then growing back up toward the wet substrate (hydrotropism).
Inspection of the references reveal the roots were of "Agravitropic roots of a pea mutant". The pea was mutant in that it didn't have the capacity to respond to gravity. I've found no evidence that normal plant roots nor grass roots could do this. But even if they could, how likely is it to have a situation where the top soil is wetter than the deeper soil over a long enough period of time for the roots to respond and grow in that direction?
So for the "deep and infrequent" theory to hold water, the roots of "shallow and frequently" watered grass would be expected to grow first down, then up towards water, then after encountering light, back down again, then back up to find water, etc, etc, etc in the zig zag pattern for the life of the grass. This is, of course, assuming one could hold the water on the surface without it sinking down in or evaporating away. And it has not been demonstrated that hydrotropism can overpower gravitropism without an agravitropically mutated plant.
MSU study:
From: http://archive.lib.msu.edu/tic/mitgc/article/2001101.pdf
Common irrigation recommendations for turfgrass are to irrigate deep and infrequently in
order to achieve a deep root system that will be better suited to endure prolonged drought conditions. Deep infrequent irrigation is a vague description but generally refers to applying large amounts of irrigation, 0.5 to 1.0 inch or more, in a single irrigation. Irrigating deep and infrequently is not recommended for all turf situations. Turf grown on sandy soils should be irrigated with smaller amounts of water more frequently as deep infrequent irrigations could potentially result in losses of irrigation water through leaching. Also, turf grown on fine textured soils with low infiltration rates should be irrigated with smaller amounts of water more frequently to avoid run-off and puddling on the surface.
The alternative to deep infrequent irrigation is light frequent irrigation. Light frequent irrigation would be described as applying small amounts of water, 0.10 to 0.25 inch, every day or every other day. Common perceptions of light frequent irrigations are that they promote shallow rooting in turfgrass thereby making the turf more susceptible to dry soil conditions. Furthermore, frequent irrigation applications are often implicated in increased weed interference. Despite all the negative effects put forth for light frequent irrigation applications there are some positive effects. Research by Melvin and Vargas (1996) revealed that light frequent irrigation treatments, 1/10 inch every day at 12 p.m., reduced the symptoms associated with Necrotic Ring Spot. Jiang, et al. (1998) also found that a light daily irrigation resulted in higher turfgrass quality, and reduced brown patch incidence when compared to deep infrequent irrigation based upon returning 80% of evapotranspiration weekly. Daily irrigation treatments have also been shown to have a smaller thatch layer than weekly irrigation treatments (Melvin, 1991).
In order to answer the question of deep/infrequent vs. light/frequent irrigation a research study was established at the Hancock Turfgrass Research Center in 1999 to compare the effects of the two irrigation schedules on three turfgrass species.
Materials and Methods
In 1999 irrigation and fertility treatments were initiated on Kentucky bluegrass, tall
fescue, and perennial ryegrass. The three irrigation treatments were no irrigation, 1/10 inch applied daily in the early afternoon, and 0.7 inch applied weekly at one irrigation event. Fertility treatments were different amounts of urea and one treatment with com gluten meal.
Results
Results from 1999 can be found in the 70th Annual Michigan Turfgrass Conference
Proceedings (Vol. 29). Trends from 1999 indicated that the daily irrigation treatments resulted in higher turf grass quality and density than the weekly irrigation and no irrigation treatments. Results from 2000 were inconclusive due to the frequent rainfall experienced in East Lansing. Research will be continued in 2001 to determine the effects of irrigation and fertility treatments on turfgrass species.
0.1 inch applied daily resulted in a better lawn than 0.7 inches applied weekly.
Other Studies
Study #1
From https://dl.sciencesocieties.org/publications/cs/abstracts/29/6/CS0290061536
Field studies were conducted to determine responses of ‘Rebel’ tall fescue and ‘Reliant’ hard fescue to deficit irrigation and irrigation frequency. Turf growing on a Satanta sandy clay loam soil (Fine loamy mixed, mesic Aridic Argiustoll) was irrigated at 50, 75, or 100% of potential evapotranspiration (ETp, i.e., turf water use when soil moisture is not limiting) on 2-, 4-, 7-, or 14-d intervals. Small weighing lysimeters adjacent to plot areas were used to obtain ETp rates. Both species performed best when irrigated every 2 or 4 d at 75 or 100% ETp.
2 to 4 days? That seems frequent to me. More so than 7 to 14 anyway.
Study #2
From http://horttech.ashspublications.org/content/16/3/466.short
'Aussie Green' and 'Celebration' produced the highest TQ rating (>7) at week 4 when watered daily. After 4 weeks of the 5-day irrigation interval, all cultivars showed unacceptable quality ratings (<7).
Based on these results, irrigating bermudagrass in 5-day intervals should be carefully monitored.
I thought bermudagrass is a weed... I can't kill it with fire, brimstone, a bottle of acid and a box of salt,,, yet the recommendation is to "carefully monitor" it with a 5-day irrigation schedule?
Study #3
From https://dl.sciencesocieties.org/publications/aj/abstracts/58/6/AJ0580060559
Dry matter yield was not markedly raised by regular nitrogen fertilization, unless irrigations were applied frequently
Food without water = no growth? Makes sense to me.
Infrequent irrigation of fertilized plots produced a lawn of only slightly reduced quality compared to that obtained when frequent irrigations were given in the absence of nitrogen
So, if we fertilize and withhold water, the lawn will look not quite as good as a lawn that is simply watered more frequently? I guess that makes sense too.
Study #4
From https://dl.sciencesocieties.org/publications/aj/abstracts/73/1/AJ0730010085
Delaying irrigation until the onset of temporary wilting, caused a significant decrease in water consumption and growth (up to 35%) in most grasses.
That makes sense... grass that is half-dead from thirst probably will use less water and grow less.
Study #5
From http://onlinelibrary.wiley.com/doi/10.1111/j.1439-037X.1995.tb00216.x/abstract
In conclusion, hard fescue had a shallower root system, shorter plant canopy, slower growth, and transpired less water to make it more drought tolerant. Tall fescue, with a deeper root system, longer plant canopy, faster growth, and greater water transpiration, is less drought tolerant at medium and severe stresses.
Hmm... So who wants deep roots anyway?
In Conclusion
5 studies + MSU + the 3 studies MSU quoted = 9 studies showing benefits of frequent watering. Frequent is a relative term, but I haven't seen any studies recommending a frequency greater than 2-4 days (most being daily). Even if I have to drag the hose around every 2-4 days, to me, that still seems pretty frequent.
I can see no reason why this issue would open for further debate. Every angle has been covered, from biology to observations in nature to real-world experimentation. I have not discovered a substantiated reason to believe one should water lawns "deep and infrequently".
Recommendations
For the best lawn appearance, don't wait until the lawn is showing drought stress, because at that point, its not the best looking lawn, obviously.
Don't water deeply. By watering deeply you're washing soil nutrients deeper into the soil. This is especially so with nitrates (NO3-), which have a minus charge and are easily leached into groundwater because the clay particles also have a minus charge and will not hold the nitrates in the soil. So by watering deeply you're wasting nitrogen and you're polluting the environment.
From https://dl.sciencesocieties.org/publications/jeq/abstracts/20/3/JEQ0200030658
Analysis of soil water from 15, 6-m continuous cores showed that as much as 95% of the NO3 applied in late August leached below the turfgrass root zone.
Maybe the reason light frequent waterings makes grass grow better is the grass gets more nitrogen, instead of it leaching beyond the rootzone.
Whatever the reason, deep and infrequent watering is the absolute worst way to water.
Credibility of university extensions:
Here we have two universities giving opposite advice:
http://www.turf.msu.edu/irrigation-practices-to-preserve-water-quality
http://www.extension.umn.edu/distribution/horticulture/DG2364.html
Lesson: Always look for studies and read the studies. Don't believe conjecture.