One of the big misunderstandings of healthcare is that even under a non nationalised system, other people will almost always be paying for your treatment.
Think of a fully privatised health insurance model - the premium you pay each month, over a lifetime, would still never be enough to cover one very complex health issue like cancer where the costs can run into the millions.
So whilst people in the US think they are paying for themselves, and reject the idea that they should pay for others, they manifestly are. Unless they're fortunate enough never to experience serious illness or accident, or simply have millions in personal wealth to cover these possibilities out of pocket.