That is true, up to a certain extent. I'd say that at university, about half of the medical students I met had one or sometimes two parents who were doctors. The rest seemed to come from comfortable middle-class backgrounds.
In my case.... my dad is a doctor and it was sort of expected I become one myself. Its not my thing though, or it wasn't at the time so now (like a lot of people on this forum) I work in engineering. In a way I do regret it now, because I wish I did something "useful" to society.
My younger sister however, did go to med school and is about to finish. She was very driven from a young age - I don't remember her saying she wants to become anything else but a doc. When her and my dad talk, I feel a little left out and only occasionally I have the feeling they look at me and shake their heads.