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I know that you're just guessing, but I find it hard to believe that there's a SOM that limits its students to coming from 6-10 undergrads.
Most of the spots below median are for URMs or graduates from tough elite schools. State schools are rarely considered (Edit: for these below median spots) unless you have significant connection or extraordinary EC.
However, I can assure you that the top tier school list we try to recruit from includes mostly top private schools, even though the list has been adjusted periodically. The list includes no more than 5-6 schools.
bdm said that there are (less than ten) schools that give you a bump on your GPA. That's it. IIRC, he and I agreed that bump was certainly no more than .3.