> These days the medical schools try very hard to make the population of graduating doctors look like the population they are going to treat.

I recall reading about some researchers that studied patients at a large walk-in clinic in a low income area. Both the set of patients and the set of doctors were diverse. Patients were randomly assigned to doctors.

What they found was that patients were significantly more likely to follow the doctor's instructions after the visit (such as getting prescriptions filled, following the doctor's home care instructions, or coming back for follow ups) if the doctor was the same race/ethnic group as the patient.