This actually isn't remotely true. It's far cheaper to buy more nutritious foods from the grocery store (especially in bulk) and then cook your own meals: http://www.leannebrown.ca/good-and-cheap.pdf
You can't have organic beef every night, but you can nutritionally and calorically out-gun fast food for the same (or a smaller) amount of money.
But if I'm poor, the difference between a ten-pound bag of potatoes and one fast-food meal can really matter.
A also believe that healthy meals can potentially increase my lifespan and quality of life within that lifespan. (I don't know if science backs this up). When I cook for myself I'm assured that cheap by unhealthy foods are not hidden in my meals - even the most expensive restaurants won't do that. (Trans fats and excess salt are two examples)