"Since they control the budget, they do get oversight......"
Oversight does not mean that they get to know what's going on, except in very general terms.
Which means they get the right to know nuts and bolts stuff.....especially since they can cut or slash the budget, they are supposed to (but fail to) make sure the money is spent appropriatly and that the agencies do not abuse their authority.
Congress though, in the real world, fails at any kind of oversight, and leaks like a bathtub thats been hit with a jackhammer, it engages in partisian warfare and is wholly imcompetant.
That said, don't be surprised to see one of 2 things happen with congress and the NSA, one is for them to move on and target the CIA again (since they are to stupid to realize the US has more then one intelligence agency) or 2, threaten to cut the budget and withold funding for the NSA unless they get answers they want (I don't mean the truth either, I mean they want to hear what they want to hear).