I agree with Lepium, it's all relative. If you are at Stanford and you cannot get an interview or land a job because you are a schmuck on wheels, you'll have an even harder time getting an interview or landing a job at some random lower ranked school because you'll still be the same schmuck, just at a different school.
Alex may be correct in that ultimately it comes down to the individual, but the reality is that you can't change who you are. No matter where you go, there you are. If you are at Stanford, you'll have the reputation of that school to supplement your resume. If you are at Harvard, you can add that to your resume. If you are at XXX then you have that going for you. Whatever XXX is, it's not as good as having Harvard or Stanford on your resume.
If you're a smoothie that could squeeze multiple offers from top firms with an MBA from Oklahoma, you can certainly get the same offers and more if you have an MBA from Stanford. If you're a schmuck who couldn't get into the K-mart management training program (I know they're not around any more) with an MBA from Harvard, you'll have even less success, if that's possible, with an MBA from Chico State.
So whatever school you're at, you'll be bringing your own history, work experience, college record, interview skills, personality etc. to the party. That's not going to change. At this point, more opportunities will be available if you can tack an ultra-elite or elite MBA to the top.