They certainly do differentiate, and any med school adcom will readily admit it.
Just look at the med schools in California, all of which are extremely competitive. Cal State students are extremely rare, and some/most? of those admits have a hook.
All of which are true, but the other factors really come into play in LS admissions for those with numbers below one or both medians. The “need” for an interesting background is much less for those above both 75th percentiles, regardless of which college that they attended. 