Yea, in general, to get into a competitive school, you already have a lot going for you: namely a stable enough home life, and supportive enough and enriching environment that you can dedicate yourself to applying your intelligence to creating a competitive application. It's kind of weird, the people that get into the schools are the ones that "need" them the least.

Conversely, there is some evidence that less privileged students have worse outcomes if they attend an elite school (compared to lower tier schools) in a substantial amount of cases where these students have not prepared to the same level as peers that have undergone a more competitive selection criteria.