I write this as a senior in a non-binding BS/MD program from an undergrad less well-known than Rochester with an MCAT and GPA requirement, who did end up applying out and got into multiple top programs (T5/T10/T20).
Undergraduate prestige is not nearly as important as you may think, that is, assuming you are dead set on medicine (not that it's to say that it is incredibly important for other fields because there are certain field where the value of prestige matters a good bit).
If I were you, I would take the non-binding REMS program for a couple reasons:
1. Advising, support, and resources for REMS student at a public institution is most likely funneled to students in your program. This includes research, scholarships, and other opportunities that would be beneficial to you.
2. As long as you do not get complacent, your applicant will be just as strong. You'll be able to start thinking about what kind of doctor you want to be - not necessarily in terms of a specialty, but how you will be working in the medical scene? Politics and public health? Community health? Academic medicine? Research? You are at an advantage, whereas many of your peers are going to be crafting a narrative as to why they want to go into medicine. You're already in.
3. Since the REMS program is non-binding, this means you will be free to take the MCAT and apply out to schools that may give you much more financial aid, better location, an education tailored more towards your goals, and etc. Compared to my peers who haven't applied out, who have applied out but didn't end up making it out, and those that successfully applied out, the ones that found the most success were the ones that hit the ground playing the game as if they were intending to apply out, not deciding on whim early on as a Sophomore or Junior.
As a disclaimer, I'm merely a student myself that is very early on this journey, just a step down the road of you. That being said, yes, a lot of top programs, during my interview trail, I've seen people from prestigious universities ranging from Ivies to Ivy-status undergrads and excellent programs such as Emory. That being said, I would say it's mostly selection bias and opportunities/resources that these prestigious places may provide, which I assume you will get no shortage of as a REMS student at Rochester.
