There's something which extreme competition does which breaks that, both by whom it selects, and by how it changes culture. MIT a quarter-century ago was much more honest than MIT today. Peer institutions -- one stop down -- are also still much more honest, although I suspect that will change in a decade or two.
The same change happened in several of MIT's peer schools.
Big SaaS providers offered us 40k each to get on board with some all-in Cloud offerings. I'd bet my hat some of the offshore IT companies we used were throwing kickbacks to Ops Managers.
Not speculation, either -- there were executives fired for such things. One set up a shell company and was billing it for consulting services to the tune of 400k per year. He got busted and probably faced charges, probably.
The competition needed to be an executive at a F500 multinational extreme. There are many good studies on the topic, from "Dictator's Handbook" to "Power." The latter should be read with a grain of salt, but has helpful insights.
Elected politicians -- above some level -- operate under analogous constraints too. If you don't take an election donation in return for political favors, your opponent will.
I think the decline of the integrity of MIT (as for executives and politicians) became inevitable once competition and $$$ reached a certain threshold.
While this might be true, I suspect the statistics are not that different from the general population.