Large numbers of US citizens don't have anything resembling "papers," and most of those who do don't carry them and would probably find it hard to locate them in the midst of a stroke. US immigration is a bureaucratic mess, and even people who are mostly doing it right get things "lost in the mail." I'm pretty sure I once worked in a foreign country without all of the appropriate papers due to some miscommunication. I worried a bit, but mostly
didn't worry that hospitals would refuse me.