It's all on you buddy. Campbell is a brand new school, 1st graduating class, and someone from there matched into CaseWestern for AOA/ACGME accredited Dermatology. I believe someone from MUCOM (I think) also did as well (MUCOM also graduating their first class).
These schools have no reputation, no previous students go to these residencies, the residency is in a different state so I doubt that faculty from either of these schools knew the staff and attending sat CaseWestern, AND they still matched!!!
That should be evidence enough that it's much more what you put into it/ what your personal capabilities are than to the institution you attend, at least for the upper echelon.
BUT, there are hidden gem perks in each school, especially those with GME. Ex. I think PCOM usually takes 1 of their students for their own ENT program for at least 1 of the spots, I also think that for WesternU they hold about 2 spots at Loma Linda for Psych (this is pure speculation, may not be true). CCOM someone mentioned has 4 ortho surg spots in a program that exclusively interviews their own students, etc etc. I wouldn't be surprised if at least 1 of the 2 Derm spots created by CUSOM goes to one of their students each year.