Really? I would naively expect the outcome to matter a lot more. As a PhD, your work product has a lot more transparency than B.S./M.S. degrees, because people

Really? I would naively expect the outcome to matter a lot more. As a PhD, your work product has a lot more transparency than B.S./M.S. degrees, because people will actually hear about your work if it matters (for several different, valid definitions of "hear about" and "matters"). However, I would also naively expect the name of the school to correlate with outcome, but only because because different professors work at different schools.