On the note of politicians being smart because they get their degrees at Yale or Harvard:

In all actuality, the biggest and most important thing about those universities is A) prestige and B) connections. From my understanding, smart people DO go there, but by and large they are schools for the social elite, not schools for the genius.

It's similar to how you're expected to develop connections in law school as well as learn since most folks who go to law school are wealthy or know someone that's wealthy (read: you're friend with a guy whose daddy owns a law firm, so you might get a job).