You could say this 30 years ago, but it's not really the case today. The majority of physicians are now salaried, not independent. And even for many of the ones in independent private practice, the amount they make is not necessarily tied anymore to the services they provide, due to the rise of capitation and other forms of bundled service agreements.
Nowadays, it's actually statistically more likely that you receive care from a doctor who has an explicit incentive to undertreat, because they receive a fixed amount of money per patient per year, and the costs of treatment come out of pocket directly with no additional reimbursement.