I obviously can't speak for other fields, but at least in my field, "peer review" means that the people reviewing your papers are from all kinds of academic (and sometimes industry) settings; it's not like it's just a bunch of MIT professors criticizing all submissions and discriminating based on the authors' credentials. For instance, here is a program committee that I'm on right now for a top conference in my sub-field ... you can see for yourself which institutions people come from:

http://www.educationaldatamining.org/EDM2016/committees.html

The chances of your paper being reviewed exclusively by "top credential" people (whatever that means) is astonishingly low; reviewers come from all sorts of institutions around the world. Even if someone exhibited an "elitist" opinion in discussions, they would be summarily shot down by the majority of people on the committee, who are not from top-ranked institutions. Again, N=small personal anecdotes, but in paper/grant review meetings I've sat on, I've never seen this to be an issue simply because most members are not from top-ranked institutions.

The same is true for NSF grant reviewing in the U.S.. Again, different funding agencies have different models, but the NSF is a peer-based model just like papers.