There are exceptions. In the case of places like MIT and CalTech, you also have access to technology you won't have at a state school. Even as an undergrad.

There's just so much research going on at these schools that you can get your feet wet before you have to decide on a graduate degree. That can be incredibly rewarding.

But yeah, for the most part you're getting connections by going to "elite" schools. Especially Ivy League schools.