> if the patient is from a place that has a national system, they pay
This obviously varies by country. E.g. for travel within the EU, a country will pay for their travelers healthcare. I live in Japan, and while the universal health insurance will pay for treatment sought outside of the country, they will only pay what it would have cost if it was performed in-country. So that doesn't help travelers to the US.
That was hearsay from a foreigner who, it seems, may have not had all the facts. Looking around, it looks like while not impossible, it's unlikely the State Dept puts much weight on outstanding (medical) debt: from reddit:
On the other hand medical bankruptcy is sadly frequent in the US so international patients isn't really a concern.