This list really highlights how important it is to go to a top school...
There are many academic benefits from attending a top school and I would advice any of my students to attend one, if admitted.
But do you need a PhD from a top four school to get the Sloan Fellowship? No. Off the top of my head, John Iaccono (Rutgers), Boris Aronov (NYU), Erik Demaine (Waterloo), Subhash Khot (Princeton) and Dimitris Achlioptas (Toronto) are recent theory awardees who did not graduate from a top four school.