A cardinal rule of medicine is that if doctors do not want to treat a patient, they do not have to, and they do not have to cite any reason whatsoever.
But then again, before HIPAA there used to be a sacrosanct doctor-patient confidentiality. W. Bush decided that terrorist doctors and terrorist patients had to be stripped of that confidentiality, or the terrorists would win. So now every two-bit cop with an attitude, all the way up to the Attorney General and his Just Us Department can read your medical files whenever they want to.
So yeah, enslaving doctors will happen if they want to. They may even try to pass some law restricting doctors from leaving the state unless they post bond or leave their families as hostages or something.
HIPAA was passed in 1996.