I've heard a major misconception about potatoes wanting full sun, but they're so short, and suspect that they grew wild in the understory of forests. Is this true, or should they be grown in full sun due to how we abused them over the history of its cultivation?
According to a paper from 1954, the wild potato was considered a ruderal species. Although found in a wide range of habitats, most of the time they were found in places with disturbed vegetation. So it was most likely not a plant living in the shade of forests, but a ruderal species colonizing new disturbed areas where full sun was available.
So for a good crop my advice is to grow your potato plants in full sun.
I'm not sure that "potatoes wanting full sun" is a misconception - there's a few things to take into account here. The major thing being context.
Being that it is 2019, that potatoes have been cultivated for between three and seven thousand years and that potatoes are the 5th most important crop worldwide(meaning that it is massively produced), I will assume that you are referring to the average potato that any commercial or recreational grower could use as a seed potato to grow for food.
I will also assume based on the nature of your question that you are interested in how potatoes originally grew without interaction from humans, so I will take that into account with my answer.
James Nienhuis is a horticulturist who has studied have different fruits and vegetables have changed over the years, noting that it is a difficult study since fruits and vegetables don't preserve as well as other things like grains. Here's an article about how some fruits have changed, probably the most well-known of these is the watermelon. While this article doesn't touch on potatoes, a parallel can be drawn between potatoes and corn. Corn was originally very small until Native Americans domesticated it and selectively bred the plant over generations until they had maize, a plant with much larger kernels that held a much higher nutritional value. Wild potatoes which Darwin noted in his research, had very small tubers that would mostly fall apart during cooking. One could assume that the wild potatoes went through a similar process as maize to produce a plant worth cultivating.
One thing that most people don't realize is that potatoes grow fruit. They look like green cherry-tomatoes, and are very poisonous but they contain a lot of seeds. This is how new potato varieties come about, while the seed potatoes grown from tubers propagate into clones, the propagations from the tubers produced from seed will be new varieties. For the most part, a home-gardener is unlikely to ever see one of these - a lot of modern varieties are sterile and even if the variety you're growing isn't, they need very mild temperatures (mostly below 80 degrees farenheit) combined with humid atmosphere.
To give an example of another plant of the Nightshade family, which is not grown as its original ancestor would have, the pepper plant usually lives for many years in an environment that is warm enough all year, but in other places like North America it is grown like an annual, unless the grower decides to overwinter it (which I have done with an Eggplant (another Nightshade) and is a really fun experience).
When looking into this stuff, one has to take into account the fact that what we have now are the domesticated versions of their ancestors. Cows now have to be milked every day, unlike their ancestors who like all other mammals only produced milk for their offspring - which is a huge benefit for us humans, and doesn't harm the cow as long as it is properly taken care of. Every thing we grow now is domesticated and because of that we get bigger food yield, hardier plants, more disease resistant plants, and tastier food - compared to their ancestors, they are definitely tastier - a home gardener planting heirlooms versus a company planting a disease-resistant variety with thick skins easy to ship is another aspect of how tasty the food is.
Potatoes can grow in an area with little sunlight. The plant will look similar to one out in a field with full sun - it may perhaps become leggy to a degree, but it will grow just fine. What will suffer is the tuber yield. A potato plant is like an iceberg. Just because it is a "short" plant, doesn't mean that it isn't using all of the sunlight it's receiving, it's just pumping its energy underground into the tubers. Which makes sense because that's how the plant species survives, letting the tubers propagate. (This would have been selected for in an evolutionary point of view, since the fruit requires such specific conditions.)
To answer the question:
Back to the literal question, wild potatoes originally grew in South America, concentrated in Peru and Bolivia. They grew in a range of diverse soils and climates, including major diversity in altitude (from the coast to very high mountains). As for the amount of sunlight they received, I can't find any sources with an explicit area, but we can hypothesize that since they grew in such a large range with so much diversity, they probably grew in harsh sunlight as well as under the shade of forests. Once the wild potatoes were domesticated though, the South Americans grew them similarly to how we do now. In large, open fields in direct, full sun.
The origins of the potato are fun to learn about and informative - but be happy that potatoes are domesticated and are not their ancestors. Grow your plants in full sun if you want a sizable yield. But gardening should be fun - grow one or two plants in shade and see how differently they grow and produce as an experiment (I would be interested in the outcome). But don't grow your potatoes in shade because the ancestral wild potato might have - you wouldn't want to put your domesticated dog in the forest to fend for himself as he is no longer a wolf.