the bias is due to a number of factors, many generalities (since many from non-selective colleges get into Vandy, as shown by the link in a previous post):
1. students from ivies (and to humor you, schools like mine) tend to have better mcat scores than those from public schools
2. students from ivies tend not be concerned with money in the first place (tuition paid by parents or lack of concern about debt) so they choose places like Vandy over U of TN
3. students from ivies tend to be more "academic" so they do research and such more often, Vandy likes this since they want to produce academic physicians.
4. as said before, Vandy has less competition from comparable schools in the region: WashU, Baylor, Emory, and Duke are the only other top private schools in the area. this is why WashU has such a high mcat average, there is much less competition from nearby top schools that one sees with Hopkins, Harvard, Columbia etc which are all relatively close to each other.
I stand by my assertion that I don't think there is a bias against anyone that goes to a state school, I'm sure that the fact that I goto a top tier LAC helped me get in, but I'm more sure that things such as my research experiences, academic record, community service, and leadership roles were a much larger factor to the adcom than the fact that I goto a top 50 LAC.