Unless there are serious reasons not to, pick the best school you get into.
I was looking over the multi-year residents list at my daughter’s top program. It’s a who’s who listing of UCSF, Stanford, Harvard, Yale, JHU SOM grads. There are about 10-20% of grads from non-elite med schools, but they’re not from low-tier meds either. Their med schools are more like top 50. Interesting though, there are 3 from med schools outside the US (not Caribbean!!! Lol ).
I still think it’s significantly stats-driven, along with research opps, LORs, grades.
Of course those who attended Harvard-like med schools are going to be more likely 250+ scoring Step students than those who attended low tier SOMs. This is what these elite school students do...spank standardized tests and excel at academics. But since there are students from med schools like University of IL Chicago included, it can be safely assumed that students like that had impressive stats too.