It can't be a pretty poor generalization when you say the same thing: "In general, I will say that at any of the "elite" schools there is a large proportion of students who had a leg-up b/c of alumni connections".
What I was saying is that the undergrad programs at the Ivyies are not really that different then any other schools. Of course you will have your percentages of very smart folk, your jocks, your middle of the roads - but you also get a lot more money students and connection students because they are the ones who can afford to pay the Ivy cost.