Personally, I think the biggest tragedy for low income people is that many small food stores that accept food stamps do not stock healthy foods well, instead favoring higher margin junk, processed food: http://www.nytimes.com/2015/03/21/opinion/see-no-junk-buy-no....
There is also the problem that a lot of healthy food is ridiculously overpriced, catering to the upper middle class population who wants to "eat healthy" and believes some nice "feel good" marketing material instead of careful thought. There still exists very good food that is very cheap, such as the beans mentioned in this discussion. Lentils operate in a similar fashion. It takes effort to identify such things though.