I had a dentist pull that on me, I told him off, and went to another one. (He wanted to pull my wisdom teeth, I told him there was nothing wrong with them, and there still isn't 40 years later. Not even a cavity.)
In some countries, such as the UK, doctors are generally salaried employees.
This is not true. A GP practice is a private partnership like a legal chambers which bills the NHS for its services. This fact is strangely overlooked by people angry about “privatising the NHS”, it’s always been this way.
It's an issue with all forms of health care. If a hospital makes money for each test done, the financial incentive will be to run a lot of tests.