I don't have a strong opinion about whether junk food is "truly" cheaper than "healthy" food (I cook every night and think it's generally a good idea for every family to get into that habit). I think it's a kind of a moot point, because what many poor families really lack is a history of having time in their schedules to cook. Cooking is a skill built through repetition and serving home cooked meals is a habit that is hard to establish.
What does bug me though is that every time this topic comes up, some nerd hits Google and finds either (a) some ludicrously unrepresentative price sample ("you pay $6/lb for chicken? i can get new york strip for $5.50!") or (b) some combination of beans and millet that will feed them just fine for a month on $3.
It is not enough, to win this argument, for the math to come out slightly in favor of home cooking. Home cooking needs to win on all three axes:
(i) price: home cooking has to be invariably comparable in price to McDonalds to win,
(ii) convenience: it's got to be straightforward to cook and to serve, bearing in mind that one of the hallmarks of low-income working families is shift work, and
(iii) palatability: this doesn't mean "it has to taste as good as junk food" (although realistically that is a factor); it means that you have to find one dish that you can serve four people and have them all come away satisfied.
None of those are easy to accomplish. Erin & I work hard to achieve any two. All three?