I can't speak for...
anything about Chomsky. I really could care less, to be honest with you.
But being in the cocoon of public and/or private school explains quite a bit about what makes the culture. There are other examples of this in society so it's nothing new. The "career politician" group can face a similar test.
I love the come back to this: but you can never eliminate all bias! - as if I'm asking to eliminate all of it. How about just shinning some light on it for all to see? How about exposing it? It's happening more and more and people are seeing it for what it really is, instead of making the blank assumption that there actually are checks and balances in most corners of our professorships, media, etc.