I agree with the responder but would like to add another opinion. While dissertation and advisers are important in a T-15/20 program, pedigree is also super important. When you start getting into lower ranked universities, who you know (advisors and networking) and how good your work is and what experience you have (presenting, writing, etc.) becomes a much more distinguishable factor that may (or may not) work well in your favor if you want a TT job. While people may assume that Dr. John Doe is great and well educated because he went to Top Ten University, it's also possible to "compensate" for this bias by doing other work that cannot simply be ignored (such as presenting, publishing, great research focus, etc.). So yes, it's harder, but not impossible.
(but also yes, if you're not focused solely on a TT job, if you can find a program that is a good fit for you, don't worry as much!)