Not all doctors, etc. were killed - some escaped the purges and were later elevated to relatively privileged positions, like Hermione's parents who get to travel between camps etc., when Voldemort and his followers had to become realistic about the fact that they couldn't leave vast numbers of people as a laboring class with no support whatsoever in the realm of health and well-being, no matter how awful the conditions would be. Hence Muggles doctoring Muggles.

- Hermione's player