I'm not sure that's really true in CS. If you're not UCB, Stanford, CMU, or MIT, you're not a "top" CS dept whether public or private. Georgia Tech, U of Washington, UC San Diego, UIUC, UCLA, UT Austin are all credibly somewhere in the top 20.
As someone who spent time at MIT and Georgia Tech, MIT may be a bit better but the difference in quality of labs, resources and faculty is pretty small, with lots of cross pollination between the schools (exe: Thad Starner jumping ship from Media Lab to GT). I don't think you could credibly call GT anything but top tier unless your only resource is Hacker News or you're focusing on one of the few sub-disciplines the College of
Computing (yes CS is its own independent college, not merged with EE) doesn't have great coverage of.
In terms of actual quality, that's probably true. I've worked with people who absolutely won't hire anyone who didn't go to one of the "top 4", and that's the sort of mindset I was addressing. It's not an "ivy only" mindset, it's a "Stanford-Berkeley-MIT-CMU only" (and sometimes not even CMU and Berkeley) mindset.
Ah, the hiring equivalent of "nobody ever got fired for buying IBM". I've seen the same with people only hiring Harvard Business School grads. I figure school-based hiring practices like that are a pretty good indication of poor management quality.