this is just my personal take as an american. I think the disconnect has to do with locality/proximity. americans who have some surplus income (ie savings and not living paycheck-to-paycheck) are quite willing to help people they know with cash or free labor and will happily donate time or money to help people in their broader community. what americans hate is being forced by the government to help people far outside their circle. I think partially we are suspicious that the money doesn't get where it's supposed to go intact, but there's also an element of "fuck them, what do those people over there have to do with me?"
obviously this is suboptimal as entire communities can be disjoint and have serious imbalances in funds available. also it tends to leave a lot of efficiency from scale on the table. but perhaps this at least explains some of your bafflement.
It's actually quite baffling how Americans generally seem much more generous, warm and helpful to their fellow human beings, but the idea of potentially paying for someone else's medical treatment seems absolutely outrageous to most.