If this were true we would expect hunter-gatherers eating their traditional diets to become fat if they have had plenty of food for, say, the last seven years.

I don't know a lot about hunter gatherers, but it occurs to me that "plenty of food" for a hunter gatherer might be very different from "plenty of food" for your typical Westerner.

In a typical American city, you can walk a a couple hundred feet and buy extremely tasty food equal to half your day's caloric requirements for an amount of money a typical person could earn in 10 or 15 minutes. So the cost of food, in terms of time, mental and physical exertion, inconvenience, etc., is extremely low for your typical Westerner. Even if you live in the sticks, it costs very little in terms of money and exertion to get in your car and hit the drive-thru window at MacDonalds.

For a hunter-gatherers, I doubt it's anywhere near that easy to eat -- even in times of plenty.