Apart from anything else, some members of the "elite" are actually smart and driven enough to be able to parlay their early life advantages into meeting the academic requirements of top schools, and those who aren't tend to end up with top school alumni running many aspects of their affairs for them anyway. Especially if they're the sort of elites that are interested in investing in startups or being active in politics or having science endowments named after them.

Top schools are also entirely capable of attracting members of privileged elites to network at their events without shepherding them through the curriculum.