It's mostly due to the difference in what is expected of them. The average home lawn wants to be several inches long (preferably 3+, for it's own health), it gets cut roughly once a week and the most traffic it gets most days is probably the lawnmower that cut it.
By comparison golf courses, particularly in the fairway and greens often get cut daily. They are cut much shorter too, fairways at .5-1.25 inches, the green is cut at .1-.125 inches. And on top of all of this, it has to put up with golf carts, golfers and the occasional golf club ripping it up by the roots. As you can see, they're the same plant, but with two very different job requirements.
Why do the recommendations help with that?
High Nitrogen promotes tall lush growth. For a thick home lawn, very good. For a golf course, excess nitrogen means the grass puts a lot more effort into growing tall, only to be cut short again. It's not necessarily harmful, but it is wasteful of nutrients.
As to Potash:
Researchers consistently show grass responses to potassium to include root growth, drought tolerance, disease resistance, wear tolerance and color on putting green turf. These responses to applications of potassium are observed even where soil levels of potassium are adequate. Research at Ohio State University suggests that potassium applications may reduce the requirements of bentgrass for nitrogen. Thus, some of the desired responses to fertilization such as root growth, color and disease tolerance can be produced without the excess growth associated with nitrogen applications.
Source: Texas A&M
It helps the grass cope better with the lower nitrogen, the increased traffic, and the stress of being cut so short.