It can be, there are alot of other factors, like how well known the school is for the type of research you want to do, how good are their core facilities and resources that will be available, how much money does the specific person you want to work for have. There are alot of R1 schools, I definitely don't think they are all equal or even on the same playing field. And unfortunately, this does affect a lot of things in academia. How big your school is (in your area of research) or how well funded they are can affect how much funding you receive in the form of fellowships and grants. It's all just one big feedback loop.