You missed or ignored my point.

No one is saying that poor people couldn't eat healthy if they wanted to more than they wanted to feel satisfied. They're saying that given two people with the same metabolic genes, exercise level, and discount rate, if one of these two people spends ten times as much on food as the other, they will be likely to be thinner. This is because being sated with more expensive food results in eating fewer calories and better nutritionally than being sated with less expensive food, and this point has everything to do with the cheapness of carbs, fat, and sugar (which taste good no matter how prepared, essentially) relative to well-prepared meat and veggies.