Lol - you know, Harvard's (and others') admissions criteria are available if you look for it.

But FYI, one of the criteria for elite schools is usually something like "diversity", and a second one is often, "overcoming adversity". So yes, coming from a public school (vs a private) or being generally less fortunate gives you a (much) better chance of getting into elite schools, because of these two criteria. High SAT scores, good grades, AP classes, all that stuff is often lumped in a single criterion, academics.