The Pima Indians were phenomenally healthy until they began eating "western-style" food - now they have about 60% diabetes and almost universal obesity among adults. They apparently were extremely well-adapted to extreme feast-famine conditions in their desert life, but not to ours.
I guess it depends on what someone considers to be "western" or American style food. I usally think of pot roasts with potatoes and vegetables. Or baked chicken with the same, or a steak with a baked potatoe and some kind of vegetable. Cereal for breakfast, maybe a sandwich for lunch.
French cooking is considered to be very rich --- lots of high fat sauces -- but yet they don't tend to be obese from it. I think most of the obese kids wouldn't be obese if they ate well-rounded meals and had very few junk food snacks around. Certain ethnic groups are known to consume large amounts of cokes --- more than the average American does. It's not the fault of learning American habits so much as it is bringing habits with them --- maybe where the water isn't safe to drink, you become accustomed to always drinking cokes.
There probably is a genetic component too --- but it would be interesting to see what would happen if a lot of groups were served Chinese food or French portions of French foods and compare with groups eating lots of pasta and breads and those eating lots of corn and lard.
As far as the Pima Indians go I am sure if you look at their diet it is stuffed with more carbs, sugars, hydrogenated fats, and alcohol that the typical "western person". Don't include "western" children in that. There are tons of white fat diabetic "Adult' onset kids. There is no diabetes in my family anywhere except in my sister's kid. None in the fathers family either. This eating style is true of Mexican Indians and blacks (in general). BTW the link you posted talks of the shortcomings of the thrifty gene theory.
The massive outbreak of diabetes we are seeing now is due to white flour, corn syrup, soy and "modern" manufactured food.