I guess then question becomes...can a family who does not have such skills and such access afford to live healthily on less than five dollars a day per person?
I think the first question you have to answer is if an average American family will eat healthily on any amount of money. Despite widespread belief, junk food is not cheap. See this NYTimes article: http://www.nytimes.com/2011/09/25/opinion/sunday/is-junk-food-really-cheaper.html?pagewanted=all
(And I think the prices they give for the homecooked meal are significantly higher than I would pay.)
I suspect most American families would eat crap no matter how much money you gave them, because that is what our food culture has become. We gave it all over to the food processing companies. It seems like homecooking has really been looked down on in this country over the last 30 years or so. But if you want to eat healthily, you still have to cook.
I think we can also agree that such skill should be taught, one way or another - perhaps in school though I could perceive some pushback for 'the American way' (or whatever else those who breed and sell beef would come up with to fight such education). Access to healthy food at reasonable prices is, perhaps, more difficult to achieve in some areas but is probably doable across much of the country.
Grocery Outlet produces a pamphlet on feeding your family on $3 a day: http://www.groceryoutlet.com/default/bargainistablog/09-09-14/Feed_your_Family_on_3_a_Day.aspx The food doesn't sound terribly appealing to me, but I'm sure it's much better than many families are eating. Maybe such things should come with the food stamps check. Maybe such things do.
There are a lot of Home Economics skills that really should be taught to everyone. Everyone should learn the basics of financial management, cooking, and house keeping. None of these issues are that hard, for example, most of the things my wife makes are not complex. But if all the food you've ever eaten comes out of a cardboard box, how can you learn how to cook?
I have no idea what to do on the political end. It really annoys me that my daughter brings home all these preachy pamphlets about healthy eating from school, but what's on the school lunch menu? Beef Nachos and pepperoni pizza. Is that some kind of joke? But, of course, the food processing companies can write whatever they want into the laws, no matter who you elect.