As much as I like the idea of her character, it's pretty obvious that none of the writers know any actual medical students.

Nor her fans. I remember one wankfest at doctorwho wherein I got my ass jumped for saying I thought it was too bad that in none of the episodes or books did we see Martha studying in any way, shape, or form, because a) can you imagine the medical library on the TARDIS alone, much less the potential of basically studying under the Doctor, and b) that I'd be worried that a lack of reinforcement of her more recent learning could put her behind the eight ball when she got back after two years of subjective time away from the school environment.