This one doesn't get mentioned enough, I think. They'll happily sell you an outline of what you need to do to be in line with "industry best practices", where those practices are all the things your competitors are doing better than you (and guess what they'll sell those companies if they spot anything you're doing better than they are? Where do you think they learned about those "best practices" in the first place?).
It's basically a kind of weird, expensive, inefficient, unofficial business process collaborative R&D program.
That's a great elevator pitch for Gartner.
Basically they need a bunch of people who are really good at ingesting a ton of data, analyzing it, and summarizing it.
Turns out those are exactly the same skills involved in writing academic papers, which gets you good grades.
So these people really are statistically disproportionately the people in Ivy League schools and similar who also got high GPA's in those schools.
So there's some reality behind what you call a myth.
(Obviously you can still be awesome at that and not have gone to an Ivy League school, that goes without saying.)
Edit: in response to a comment below... also you can of course be at an Ivy and not be a good writer too. Which is why consulting firms tend to have extremely selective hiring on campus through interviews with many rounds where most applicants get rejected, and pay huge attention to your GPA at college.
With college grade inflation and the fear of blowback from failing well-connected ivy students, the only guarantee you get from hiring an average Ivy League student is that you have someone who can write high school essays well. The typical undergrad graduate still barely has any critical thinking ability.
If you want people fresh out of school who can ingest data, analyze it, and summarize it, you want good grad students. Good grad students come from non-Ivy schools more often than not.
The only industries that care about Ivy League at this point are the ones where connections matter more than intellectual ability. Everywhere else has recognized that the pedigree is not a useful signal (see Google’s hiring data on this).
The only conclusion you can always make about someone who graduated from a prestigious college is that many people will find this impressive. That's not to say this has no value, clearly it does.
One can also graduate from an Ivy and definitely not have these skills.
Although one might think that these folks are not consultants at McKinsey, I humbly suggest that this is incorrect — there are plenty of folks who McKinsey brings in for their social capital and/or social skills. Certain athletes and certain folks who know how to socialize with a given class of clients are just as valuable as the grinders, perhaps more so since the “face” of the organization leads to sales and client retention.
The person/human is significantly more important.
After working with duds from top schools, I'm not sure why it happens. How do they get accepted? How do they graduate? How did they get past interviews?
The other thing management consultants do is industrial espionage -- they go into a company to learn how it work, and then advise other companies on how "industry leaders" operate.