Both my parents are doctors. My parents definitely have had frustrating days where they've told me "don't be a doctor!" but many days, I learn about the good aspects of becoming a physician. There are plenty bad ones (medical malpractice, hostility towards doctors, changes in healthcare, etc); however, there are also the good reasons, like when they can really make a difference in someone's life - diagnosing a rare condition that might have otherwise gone unnoticed, for example.
I don't think it's a particularly genetic reason (as the OP mentioned), either. People like what they know, and I've grown up around medicine. Though there are many more important factors that made me choose medicine, I feel like the fact that I was already sort of 'there' in the first place was a big help.
I wonder if similar statistics might be seen with other professionals, such as lawyers or engineers.
Also, the process of applying to medical schools is VERY different from when my parents were applying to medical school (they are in their mid-50s). Back then, med school was much more affordable, and my parents don't know anything about this application process, except that it seems much more extensive and competitive than when they applied. I have no idea why premeds with parents who are doctors would be under-represented on this forum.