Even getting an interview often requires attending an Ivy League professional school or a very few top tier equivalents
Anyone could apply. All applications were taken seriously, and I worked with several excellent people from non-Ivy-League schools. It would be much more accurate to say:
Even _knowing_ about such business consulting firms often requires attending an Ivy League professional school or a very few top tier equivalents
I always found this regrettable. It boils down to the fact that most undergraduates have never heard of most business consulting firms (or the industry at all), so a lot of work (consultants' time) and money go in to on-campus awareness marketing. That doesn't scale well at all. So we ended up doing it where we had the biggest bang for the buck (in the UK, this was just Cambridge and Hull... err, I mean Oxford). We would sometimes send one new hire to the careers fair at a few other universities.
Bottom line: anyone could apply; every application was taken seriously; 99% of students outside Oxbridge had never heard of us, and that was too expensive for us to fix.