i don't know of any statistics on this issue. i doubt the AAMC is rushing to publish applicant socioeconomic data – but please correct me if i'm wrong.
the idea that affluence helps medical school applicants is a conclusion based on the strict requirements of medical school admissions. when you have to work your way through college, it becomes more difficult to shadow, perform research, volunteer, study for the MCAT, and excel in your classes. hence, many successful applicants come from wealthy or upper middle class backgrounds, because their opportunities aren't limited by financial constraints. not to mention that some of them have physician family members who can facilitate shadowing, provide guidance, et cetera.
but to answer your question, i think this is more of a logical inference supported by evidence on the interview trail, as opposed to something that has robust statistical support.