I would agree in most cases, but I do recall listening to a podcast (I think it was with the Dean of Admissions at Loyola), where she said that occasionally she gets calls from alumni/big-names that causes the admissions committee to take a second look and occasionally invite applicants they might otherwise have relegated to the "silence" pile.
I honestly think this kind of stuff happens far more often than we think. Just anecdotally, I know at one well known West Coast school, the Dean of Admissions stopped by one of the med classes after they had finished for the day and asked "hey, do you guys know anyone applying here this cycle?" An acquaintance of mine got invited this way (an ORM, and his/her stats were below their 10th %iles, although his/her EC's were great). And I've heard similar stories along the interview trail this year. It certainly helps to be well-connected in medicine.