I've worked with inner city youths, and that is completely false. If that were true, we'd expect a very skinny poor population. Instead, a large percentage of America's poor are overweight.
I think the real reason is that food generally costs a lot less than it used to cost, relative to housing and other expenses.
Poor people often know how to cook, out of necessity, and make the food taste better by retaining more of the fat, adding carbs like rice, and plenty of meat.
Food is sustenance, culture, entertainment, and reward all in one experience. And the price is relatively low. If you have $10, you can dine very well if you can cook.
[NB Genuinely interested - not being snarky]