But, once you get into the grants and peer review game, connections and credentials, unfortunately, matter a lot. It is not explicit in that no one says "hey you are from XYZ university, hence I am rejecting your paper." What happens commonly is that for peer-reviewers opinions are colored by your credentials. My hypothesis is this: if one were to control for quality of paper, a credentialed or pedigreed author's paper is likelier to get accepted than the non-credentialed ones.
There are many exceptions and there are deliberate programs like EPSCOR (for grants) to prevent such things from happening, but the inequality exists nonetheless. The inequality is sometimes justified, sometimes not.