Do they have to be Master Doctor or is trainee or adept good enough?
I've found that a Trainee Doctor will heal someone and gain skill by doing so.
I now train as many of my villagers in healing as I can manage (I just give them enough to turn them into Trainee Doctors - a bit like having first aiders around) because I found with VV1 that if I left them alone for a longish time they ALL turned into farmers and researchers and in a village of 90 I had no healers at all :(.