Note that I wasn't really making an argument, I was just presenting that clip since I found it pretty interesting. I'm not claiming that the situation in that clip is representative of the US as a whole, but still, the fact that there exist areas of the US that are in that much poverty is quite a surprise (at least to me).
At least in my opinion, a healthcare system that fails the very poorest of the population is not working, and is certainly not the "best in the world." Of course, as you say, to have a nationalised healthcare system would mean that the more well off people are subsidising even more for the less wealthy people. I think that's the way that healthcare should work, otherwise we get into a more and more elitist society where the rich get richer. However, I fully understand that you (and most other Americans) believe in healthcare, like other things in life, being earned by hard work. After all, this is pretty much the American dream.