Surgeons get privileges to work in a hospital but in general are not employed by hospitals. Some smaller communities dealing with very competitive specialties may end up hiring a surgeon but this is still an exception to the rule.
In my state, malpractice is an individual policy, even if you work for a group or hospital.
But since you bring it up, getting hospital privileges is going to be another challenge in addition to getting a license and insurance.
OK ... my thinking was based on the George Washington University Hospital in DC. Most, if not all, doctors and surgeons at the hospital are members of a practicing partnership “Medical Faculty Associates” ... so, from a corporate/liability perspective, I guess MFA is not the same entity as the hospital or university. But they are to the public and patients. It could be that just the docs who teach and practice are members of the MFA group.
I can’t imagine with Lakin’s experience, he would not be well received at many hospitals, unless they don’t want the publicity he would bring at first. His penalty has nothing whatsoever to do with his actual practice of medicine, and with the awards he’s received over his career, one assumes he’s pretty good at what he does. I just hope he lands on his feet when this is all over.