This is part of why I was so glad that the WIC program put in new guidelines that allow for fruits and veggies. It's a start, at least.
I will definitely agree that eating fresh foods costs more, but fresh is an ideal of healthy...not the only option. Note that the folks living on a dollar a day weren't subsisting on what the originally quoted article called "junk" - they were living on the staples of a low cost diet that are also fairly healthy...oats, beans, lentils, nut butters. These things do take time to prep, and knowledge that is currently lacking (one of the reasons I think cooking should be taught in school to everyone...read another really interesting article about how it is essentially becoming a spectator sport, instead of something people actually do...think Iron Chef or Top Chef). I think a lot has to be done also to get healthy food sources (rather than convenience stores) into areas with higher poverty levels.
My point isn't that it's easy to eat a healthful, less expensive diet, but that it is possible with basic equipment and some knowledge (and again, I acknowledge that many people may not have basic equipment or cooking knowledge and that is a different issue that requires different solutions).
Hillbilly Housewife is also a great resource: http://healthy.hillbillyhousewife.com/index.htm