Maybe so. But Google for "parents of dead child sent bill for airlift" - if you want to be pedantic, you can even argue that in some of those cases, there may not have been any choice, only an implied consent by law that says that "a reasonable person would have wanted to be flown to hospital".

You'll find examples. And for every waived bill you'll also hear "well, regardless of the tragic outcome, a service was rendered, and we have the right to be paid for our work".

Please note that I am carefully avoiding passing any judgment on the morality of any of the above.