In my experience, there is no truth to this. (I'm assuming, of course, that the high-stat applicants don't go to their interviews acting like they think they automatically deserve a spot based upon their stats. An arrogant attitude is the surest way to sink your chances quickly.) Medical schools are not charities. They want to accept and matriculate the best students they can get, however "best" is defined by that school. If you have excellent stats and the school feels that you will be a good fit, they won't reject you just because your stats are higher than their average. If anything, they'll accept you and throw in a scholarship offer to try to convince you to choose them over the higher ranked and more expensive schools.
I think a major key to interviewing well at a particular school is to have a very good answer to the question of why you want to attend School X. Don't *ever* treat any medical school like it's a backup or like you think that you're too good to go there; go on each of your interviews with the mindset that this could be the only school that accepts you, and act accordingly.