While there are some poor groups who cannot get any frozen vegetables or unprocessed of any sort without going into debt or becoming homeless or just not having access, I think they are the minority. Frozen vegetables, canned beans and meat, eggs, etc. are very healthy, very cheap, and ubiquitous even in mini-marts. Almost everyone can eat healthy if they really prioritize it.
The main issue is that when you’re poor, you don’t prioritize healthy foods. You have stress and much bigger things to worry about, you’re more concerned with having food than having quality food. While its possible to buy healthy, it requires finding a way to get to the grocery store and save a few dollars somewhere else. And then, the payoff is that maybe it will make you healthier, but maybe not even, because the additional stress and undiagnosed health issues may cancel it out. To top it off, the foods I mentioned - canned and frozen vegetables - are boring and not particularly tasty. If you want to make healthy food which “tastes good”, you need to spend significantly more time money: you need to go to fancier stores, pay more, actually cook the food, and make sure it doesn’t go bad.
So just giving poor people theoretical access to healthy food isn’t enough. You need to encourage healthy food with discounts, make it more accessible, teach people what is healthy, and why eating healthy food is important. And on top of that, eating healthy needs to actually be important vs. the other priorities people are dealing with.