I think you've got that right, GovernmentShrinker.
It's impossible to get a state-issued license to operate if you have no ties whatsoever to either public funding or public regulation.
The only hospital I hever heard of in the USA that doesn't have public funding entanglement is the St. Rose's cancer hospital run by the Hawthorne Dominican Sisters in NYC. To this day the sisters do not charge their patients. They do not deal wiuth insurance. Nor do they rely on government support; they accept neither Medicare nor Medicaid. What they rely on is 100% private donations ---"what the mailman brings us every day," according to Sr. M. Joseph, administrator of St. Rose's.
It’s also impossible for an individual doctor to get a license to practice medicine without spending at least one year (and realistically, four years) working for way below market pay at a hospital which provides a lot of below-cost care to Medicare, Medicaid, and other patients. And the government-protected anti-competitive national matching program will assign the medical school graduate to a particular hospital. You go where the government’s agent tells you to go, and work as many hours a week as the government’s agent tells you to (even if it’s more than the law allows), and get paid what the government’s agent says you will get paid. Only after that can anyone legally practice medicine in the US, even in a one-doctor office that doesn’t accept any kind of public or private insurance.