Hospitals certainly appear to be operated for the benefit of physicians and administrators, and their compensation is an expense not profit. The relevant statistic is highly compensated leaders, not profit.
True, though they'd still be paying payroll taxes. To me, it seems like the thing nonprofits could maybe let you "get away with" is building up an endowment that can fund sinecures, which could effectively turn it into a sort-of super IRA for the ultra-wealthy (i.e. with no required distributions for your beneficiaries after you die, you could have an effectively everlasting traditional IRA that your descendants control and could access through fake salaries). This has the side "benefit" of letting your descendants save face and pretend to have important charity work that they do as opposed to being a layabout that lives off great-grandpa's wealth. If you do it right, they might even believe it themselves!
Many hospitals never employ a single physician. Or next to zero.
Am a paramedic. All of the ED physicians in the Level 2 Trauma Center I take most patients to are not employed by the hospital, but by a collective called "XYZ Emergency Medical Providers". The hospital then (I don't know these details) contracts with the collective. I also believe, very similar to a union, that if the hospital wishes to hire a new provider, they may handle all the interviewing, but ask for the collective to hire them.
