Half of them are based in hospital or rural infirmaries as state doctors who dont receive extra payment for their services,and the other half are private ones working in their permanent consulting offices. Except tourists who want to use the basic benefits of form E 111 with contracting doctors in office during morning hours, all others with private insurance have to pay a fee to the doctor for his services and get a mashine punched receipt,explaining in foreign language, diagnosis and service done.
Fees are very reasonable, well low compared to west European standards.
Except heavy charging, due to commissions, they might drive you in trouble cause they don't usually cooperate with specialists and fall into malpractice. Beware also for false receipts. To visit a medical specialist in Greece it is the commonest practice and the norm.