In terms of CMU, I'd say your first point is short-sighted. Because of the relatively large Design/Art, Architecture, and Business programs, the generic freshman orientation/prereqs, a surprisingly inclusive Greek presence, and the small social scene there's plenty of opportunity for mixing with different people.
In fact, I'd go so far in saying that meeting people outside of your typified social circle isn't institution dependent, rather an individual preference (so I wouldn't be surprised if your generalization isn't applicable to MIT either).
Also: admissions at Ivies and Stanford work very differently from admissions at MIT, CMU, and Berkeley. The latter set of schools are more meritocratic -- you get in if you have high grades, high test scores, etc. (Although it takes a lot more than high grades and test scores to get into MIT.) The Ivies care a lot about extracurriculars, athletics, and essays. So, if you're, like, a world champion debater, that would go far at Harvard, but not so much at MIT.