Some residencies take mostly from their own med schools. If you don't believe me, check this out:
http://www.neuro.jhmi.edu/nustrn/residents/index.html
Also, I'm not sure about the details of other specialties and other schools, but I know that Columbia has a national reputation for training med students in neuroscience. I've heard this from my undergrad (UCLA) profs, a residency director in CA, and others, not just P&S folks.
Obviously, I'm concentrating on one specialty, but some of these points are probably applicable to various different specialties to different degrees. You'd do better to look at a bunch of residencies to figure out what would be good choices. Using neurosurgery again, if you look at Hopkins, the Barrow, UCSF, Columbia, and other programs, you'll see some of the same schools over and over. The main thing to notice is that programs like their own, though most aren't as inbred as Hopkins.
Anyway, you shouldn't set your sights on one residency as matching a competitive specialty is even more of a crapshoot than getting into med school. You wouldn't give up on med school if you couldn't get into Harvard/HST (or whatever your favorite would be), would you? Also look at things the other way: How many people from schools you're considering are matching in ortho, neurosurg, derm, ophtho etc? I realize that not all super-qualified students are interested in competitive residencies, but that's true at all schools, so it's not really much of a confounder. People might tell you that it's all up to you, it's just that Harvard a group of students that are preselected to be more competitive (MCAT is the best predictor of USMLE step I-there's a paper on the AAMC website) but that variation in numbers (between med schools) isn't so great to explain matching performance differences. What does? Med school.