It ain't that ridiculous. Poor people can't afford high quality raw ingredients and so more rely on highly processed, high-calorie foods (especially HFCS) that leave them obese.
Food stamp payments might be more than you think. For example, for a household of two people in California, the minimum payment is $430/month [0]. That's not going to be putting fancy food on the table, but its more than beans and rice (or soda and chips).
[0] https://www.getcalfresh.org