My mom got injured while hiking in a country with universal care. She hobbled to the next town, found a clinic, and got treated. Then she wanted to pay. First, the person at the clinic said: "What do you mean, you don't pay for health care." My mom explained that she was from another country. It turned out they didn't even have the means to take her money.
Treating a few foreigners for free might actually be cheaper than setting up a billing system.
Evidently she was not hiking in Canada, where they definitely will treat you and then make sure you the tourist does pay the sizeable (though not USA exorbitant) bill. The Canadian system in fact does have many payers; federal, provincial, private insurers, are all payers.
I'm a Canadian, but accidentally let my health card lapse right around the same time I had a fall that tweaked my wrist. At the clinic I went to, they explained that I would have to pay cash for the visit and to keep the receipt because it would be reimbursed by the provincial ministry of health once I got my card renewed.
Had a visit with a GP, he sent me next door for Digital X-Rays, and then I went back to to the GP where he looked at them and sent me home with a brace (no break).
GP visits: $25
X-Rays: $25
Brace: $15
I don't think I ever ended up submitting the receipts to SaskHealth... Just wasn't that big of a concern :)
I'm a Canadian, living in America and therefore not a benefactor of Canada's healthcare system, even if I'm visiting Canada. On a trip to Canada a near car accident caused abdominal pain for my pregnant wife and a subsequent trip to urgent care to confirm if everything was OK. The bill was $600.
Most UHC countries have reciprocal deals where a citizen of one has all the same rights as a citizen of the other when travelling. Its just a lot cheaper than having to ship people around or delay treatment or all the paperwork.
The US has no such deals because it does not have a UHC system to deal with. However, most UHC systems that do not charge aren't going to pay out for setting up a billing infrastructure for the occasional American. The ones with co-pays etc already have a billing structure in place, and may charge you. Or not, it would be pretty mortifying to have to charge someone for health care.
If you are a legal resident, you are covered. If you are a visitor it depends on what deal your national UHC system has with the nation you are visitng. Normally there would be little reason to go to a foreign country for treatment.
Treating a few foreigners for free might actually be cheaper than setting up a billing system.