Hozzle
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.
A competing setup is the Bismarck style of insurance company administered management, either for-profit or non-profit. Germany, the Nederland's, Switzerland, etc runs this sort of system. Always with a lot of legislation and safeguards to ensure that people do not fall outside the system. It is similar to the US employer-provided insurance setups.
Other systems are National Insurance, as used in Canada and Japan. Similar to Medicare. Canada is fairly unique in its hostility to private provision.
And then there is out of pocket, like rural Africa does it. That's basically like being uninsured and not qualifying for Medicaid.
Thing is, the US accumulated massive bureaucracy and costs by h\trying to run every system at the same time with little attempt at standardization and lots of billing and gatekeeping. Everyone else picked one system and stuck with it, letting private providers fill in the gaps. (Except Canada for the last)
IN most nations with a VA-style (Beveridge) setup, there is great media interest in the least failing or hint of scandal. And they mean politicians lose a lot of votes. The VA hasn't enjoyed that feedback system until recently.