You are overthinking it. Real elites, like everyone else, simply like what they know already; and they know those schools because they have been there, or know a lot of people who have been there, so they can evaluate the sort of challenges other pupils went through in a way that makes them more confident.
At its core, this is elitism in the oligarchic/aristocratic sense, not in the intellectual one.
It's not so much an issue of quality as it is brand recognition. I went to a top 20 State school, that is to say top 20 among State schools, and while, to me (if I can say so without sounding self-aggrandizing) that's a pretty good ranking, all told, not once in my life have I heard my school discussed in any media whatsoever as an intellectual powerhouse.
The top 'brands' get the largesse of the praise, and the lesser schools are left to fight for the scraps. I sense the balance shifting somewhat but nonetheless the attitude of 'if it costs more, it must be better' seems utterly pervasive.
I yearn to be proud of my education.
I yearn to be one of the 'cool kids', and I don't think it's because I have no sense of personal worth or that I am self-marginalizing. I simply think there is a crisis of hubris that we overlook in favor of pointing out instances where the 'have nots' do well.
For every kid from the hood who makes good, there are dozens, hundreds, thousands of upper management jobs handed to those who attend schools based on the meritocracy of wealth.
It is astonishing. It is the crux of why our cultural stagnation is reaching critical mass (see current President-elect for more on that topic, I mean seriously, who thinks Donny got into Wharton through acumen and not the bravado wealth affords the ineffably idiotic?).
My point is that your summary resonates hard with my own experience and I appreciate your perspective.
In reality I don't think there is any significant difference in terms of education quality between the top #1 university and #100 for any given field.
But the difference in terms of opportunities after finishing MIT vs finishing some other good university is massive. It seems that if an investor or prospective employer hears the word 'MIT', 'Harvard', 'Stanford' or 'Yale' when you make a pitch, somehow you're considered to be much smarter than the rest.
I think it's partially due to this elitist mindset. 'Elites' seem to think that people who went to an elite college are many times smarter than everyone else - But the real difference is actually social connectivity.
People who went to an elite institution are closer to capital - This gives them more influence. They are more likely to become investors and employers themselves. Their elitist world view (rooted in the false perception that they make up an intellectually distinct group) means that they are more likely to hire/fund people who also studied at elite universities.
Elites think that people like them congregate around knowledge, but in reality, they congregate around financial capital disguised as knowledge.