I have what's considered decent health insurance from my job, so even that doesn't pay nearly all the bills, were I to get sick. Going to the doctor is still quite expensive in many cases. I don't understand at all how other people in my situation wouldn't rather have the demonstrably better systems that exist in other countries.
As for the rich, well, they seem to see unfairness everywhere. A few years back, our insurance plans changed, and we all had to go to meetings to hear the new details. When pricing was explained to be tiered (3 tiers), a mid-level executive in our meeting asked "you mean to tell me that just because I make more money, I'll be paying more for the same coverage?". To which the instructor replied "I'm sure anyone in this room would be happy to exchange their salary and price with yours". That got a few laughs and a fair bit of murmuring as well.
Seeing that the room was not with him, the executive shut up. But you could just tell he was fuming over paying what I recall to be about $40 more, monthly, for him than the lowest-paid employees would be paying.