I have worked in 4 states and I see racial differences with this as well. Here in Baltimore, they went a disability check because a child cannot pronounce r correctly. The schools fill out hundreds of these each year and that is how i know. We see the same families that ask for Xmas help wasting 20 dollars on lottery tickets frequently. The worst is that they might even ask for the help within the same trip (we have a convenience store across the street from the school). And, because I evaluate children as part of my job, I do interviews with them. It is very consistent that they believe this. They exploit the system our school social workers pull together resources for a family and then go to the home to give them out only to find a huge supply of beer and cigarettes. Even though we have free school lunch and universal breakfast for all, they pick up fast food for the kids. So, it is not even a matter of them attempting to use a grocery store. I sit in team meetings where I hear it from the parents. They complain about how the government does not help them enough in one sentence and then talk about buying an expensive video game system in the next sentence. They pull out phones that cost more than mine does and still get food stamps. am not sure where you work, but it is the worst that I have ever seen it these last few years. The parents at my schools are not like the ones that you describe.
I will add that the fast food places are further than the grocery stores. They are in the same general shopping area and the grocery store is not more expensive. I do hear a lot of talk about what you describe, but it is all talk. When provided with resources for helping themselves, they do not follow through. I have been in the schools since 1994 and it has gotten worse with time.
I would agree that there is a subset of our poor that are not this way, but these tend to be the immigrants or those whose poverty came from something other than multiple generations.