That's not a fair assessment. The problem with NSA isn't that their authority is opaque. The problem is that their authority, dating back to the cold war, is so broad that it's difficult to cabin what their doing into public policy objectives.

In other words: once you pass a law that gives the government authority to dragnet communications, no matter how specific and overt the law is, the authority you've delegated does grave and intrinsic harm to transparency.

GCHQ are pretty clear what they are doing. They hover up everything they physically can regardless. If they get caught and it turns out to be illegal they get Parliament to change the law for them.