I think most of us who have done the research can recognize that being a doctor's kid does not make you "rich." It certainly has a lot of job security and affords a good lifestyle, but not too many doctors retire early, or can take extended breaks from practice because they have money in the bank. Being a doctor's child myself, I know what it's like, and I can tell you I don't consider myself rich. I've had a job since I was 16 and I have paid for my last couple years of school.
I've always gone to a public school, and never gone on anything extravagant. Heck, I've never even been to NYC, or even out of North America. I'm sure a lot of you "non-doctors children" can chalk up some of those things.
I know that I have had it pretty good--but I think the "rich doctor" stereotype is going to be one that some day you may be disappointed in... esp. if you end up having a hard time making it as a physician working 70 hours a week.