Hospital organization is a very odd thing.
Very, very few physicians are employed by a hospital. Rather the physician is granted the privilege of admitting (treating) patients in that hospital. The Chief of Staff for the hospital (a physician) is, in a sense, a boss with regard to privileges and physician behavior in the hospital.
There was a time when some physicians (radiologists and pathologists come to mind) were employed by the hospital but more often, now, they are not paid salaries by the hospital but bill for their professional services separately from the hospital bill which covers the cost of the facilities (diagnostic imaging equipment, path lab, etc). In these cases (as with emergency medicine) a group of providers contracts with the hospital to provide services at that hospital. In that regard, a hospital could choose to fire the group by not renewing the contract and choosing a new group.
Some physicians don't have privileges but practice from an office setting only.