The hypothetical was horribly put (Harvard vs. Michigan as the lower-tier? LOL) and now I need to rant.
First of all, get over yourself before you step into a lab. They're doing YOU a favor, not the other way around. Undergrads are a huge waste of time and resources 99% of the time. We bring you into the lab not because we think you'll be of any use but because we're doing you a service. Our interest in bringing you in is in the hopes that you'll eventually repopulate the field, do good work and push the field forward so that everyone benefits, whether as a Ph.D, MD or MD/Ph.D.
So don't think that you're doing ANY lab favors by gracing them with your pre-med presence. Be glad you're getting ANY research experience and work your butt off. We're fine with pre-meds in lab as long as they work like pre-meds. It's often vocalized before summer that the only reason to bring pre-meds in is that they're willing to show up on time, do as told and work hard.
Okay, I guess I should answer the question.
When you look for a PI, a Nobel Laureate could or could not be active in research. They may have burned out, moved into administration or business and may have a lab in name only (this is surprisingly common). If you do find one that's still knocking Science papers out like its job, the only distinction that is actually meaningful to some pre-med is that this lab will have tons and tons of money so it'll be less upsetting if you kill mice or use up whole bottles of reagents. We budget financial loss from undergrads in the lab anyway every summer. You will not be handheld in the least because these labs also tend to be pressure cookers for the post-docs, grad students and fellows who are using it as a launching pad for their careers. They don't care about your welfare as long as you're doing what's asked. If you do what's asked well, you could get published and then you'll likely get published in a higher-tier journal than by someone else who had the same idea and paper without the Nobel. You may see the PI all of once or twice and it's unlikely he or she will even learn of your existence unless you're exceptional in some good way. Then let's be honest. You'll probably go to graduate school.
Labs at Harvard are like labs at any other institution. You get out what you put into them. The PI in one lab could be super-awesome and interested in furthering people's careers and the PI down the hall could be using post-docs and grad students as slave labor. Does name help? Sure. Like at any other institution though, your success will be guaranteed by your willingness to do as you're told.
Letters of rec will be written by the post-doc or grad student who supervised you and signed off on by the PI. So focus on impressing them, not the PI. The PI's impression of you will be determined by them. The letter of rec trumps the name of the institution, btw. A mediocre Harvard letter will carry much less weight than say, a Michigan professor who thought you were the greatest thing since sliced bread.
What would be most meaningful is getting publications. You may do that much more easily at a nice lab at a slightly less recognizable name (you're deluded if you think Michigan is expecting less than Harvard) that is still well-known for research like Utah or Minnesota, for example. Or at an assistant professor's lab at an undergrad-focused institution like Caltech, Rice or Princeton where they are expected to train undergrads. You want to be somewhere where they are patient enough to teach you and will give you freedom and responsibility if you're a skilled scientist to do your own project. That usually happens in smaller labs with younger professors regardless of the institution.
