I've heard this argument a lot, but personally I've never been to an area in the US where you couldn't get to a Walmart or similar "cheap" supermarket in a reasonable drive and where you couldn't find basic fruits/vegetables.
Sure, it might not be your fancy organic bodega but they've got everything you need to eat right and it's not that expensive.
I mean, hell, even without fresh produce, you can buy rice, canned beans (black, pinto, garbanzo) and (non-syrup) canned fruit and that will be some of the cheapest food in the store.
It's really not that hard to eat healthy for cheap if you know what to buy.