I think the details about what a universal healthcare system should cover or not are definitely up for a debate. However, I've met quite a few Americans that are adamant about not paying for anyone's decisions that I feel they don't get the basic concept of a society, like "we all pay for the firefighters so if your house burns, they come regardless". And they weren't walking cliches of tobacco-chewing redneck Trump voters. Almost every country discusses vividly what should be publicly funded and what not but I feel Americans have a fairly unique perspective. The hate of taxes that you mentioned is definitely part of it.