Such an interesting question.
I wouldn’t say this. It would depend a lot on the department, too, especially in the sciences and engineering. But academic positions are so competitive these days that even mid-ranked schools can compete for faculty with degrees from the best places with ridiculous publishing histories and bodies of research. The research at Columbia and Penn and Duke (especially in the biomedical sciences) and at Chicago (in economics, especially) is every bit as cutting edge as that at Harvard, Yale, Princeton, Stanford, or MIT. (In fact, I would say Princeton is actually on the lower end of the research spectrum given it’s smaller size and heavier undergrad focus).
That’s definitely true beyond Harvard, Yale, and Princeton - it’s definitely true at Columbia, Northwestern, and Penn as well (I know some students from those schools who have fallen into those designations), and also I suspect at Duke, Chicago, Dartmouth, Brown, Vanderbilt, etc. The constellation of schools that earn this designation is bigger than just a handful of schools. (And goes way deeper than you might thing…I went to Spelman, a top HBCU, and I knew many students from Spelman and Morehouse as well as Howard and Hampton who had non-business majors and were recruited into elite investment banks or financial firms.)
The super-star faculty (not in terms of talent or skill, but in terms of general name recognition) and super talented/famous/noble students are probably two distinctions. The very tippy-top schools have the ability to poach super-star faculty that actually may have done most of their work or developed their agendas at lower-ranked schools. And the children of foreign dignitaries/royalty, pop stars and actors/actresses, and child prodigies do seem to be more likely to choose Harvard or Yale than Chicago, Vanderbilt or Duke. But I’m not sure that’s a particularly good reason to choose them, or necessarily an “opportunity” to miss out on…