You added another variable, school debt.
My answer remains the same. Great students can do great things almost anywhere. Some things cannot be easily quantified bc it has more to do with the individual than any other factor. (A"meh" student who just goes through the motions or the student with drive/motivation/innovation who embraces or creates opportunities…both exist in all environments.)
Based on some CC posters, a student would think the only path to high level success is through a limited prism of schools. A student interested in business and aspiring to CEO of the “largest employer of scientists and engineers” in the country would be told that only top schools lead to that path. Hate to bring LM back into the discussion, but their CEO went to UA for undergrad. 
For your med school analogy, many posters would state that where you complete your undergrad does not matter for med school.
For our own family who lives in a very fiscally driven reality, my older kids have great careers and no one has debt and we don’t have college funds. They thrive where they are planted. 
Our college “freshman,” a jr by hours, is attending on full scholarship. He could have gone to a top school, but only with what in our world equates to massive debt. I do not believe for one minute his future is going to be limited by his school choice. It isn’t about the school. It is about him. He has drive. He is bright. He knows what he wants and takes the steps to succeed. He is doing what it takes to make the most of every opportunity that exists. He is also a young man of great character. Those traits will lead the way where our limited finances couldn’t.