Yeah there's not much talk of it here in Australia but America is a ripe example where prestige is actually a very important factor to get into the bigger multinationals - It's a bit of a cycle there - basically alumni is a big thing and can really help you get through the door , not to mention prestige usually hails from overall better faculties and teaching/curriculum.
Over here you got lecturers and tutors working for 3-4 different uni's at once so generally the teaching will be similar thus the difference is much more narrow.
I agree on the basis that really university isn't that important apart from requirements for post-grad qualifications (that enoil already mentioned), rather the experience is what is ultimately more valued these days as well as the overall package.
I do argue though that the top universities have more opportunities to gain work experience and ECs though, which does help in the short-term for getting that first internship/grad job to kickstart your career.