We have a couple regulars who know way more and can correct my post but I hope I got the jist of it mostly right for the questions asked. CIA/NSA covers different types of intelligence, CIA has actual goals to where it cooperates with "enemies" depending on them, the NSA more or less has just existed to collect data with no clear end goal. (Either because it never got one, or it's shifted from the Soviets to rogue states to terrorism to who knows.)
I'd say Oliver puts too much faith in the whole "the law says the CIA can't do this!" But then again, I obviously would say that.