That's possible, but when we know that many people who are MIT Professor Good could not get into MIT for undergrad[1], it still requires us to believe MIT's admissions and graduation criteria for PhD students are very loose compared to all their other observed standards.
That's frankly ridiculous, or at least the CalTech example at the end. For undergraduate study, MIT and CalTech have a strong filtering function in that you must be able to do math and calculus based physics, and, oh yeah, one "humanities" course per term. A student brilliant only at math would likely fail horribly. And so a student who's brilliant at just CS might not make the cut for MIT, since MIT's EECS undergraduate program requires a minimum of both EE and CS (for better or worse, that's their view of what an undergraduate must have).
Change the domain to graduate programs and above and things are different.
While I'm at it, back some years ago last decade before MIT gained a lot of attention approximately 13,000 students applied a year for the undergraduate program. 3,000 were judged to "be able to do the work", and only from them was a class of 1,100 students constructed.
[1] -- http://www.scottaaronson.com/blog/?p=2003