I'm sure that when Snowden's revelations came out the first thing that happened is that the government created a new more hidden level that could not be touched

I'm sure that when Snowden's revelations came out the first thing that happened is that the government created a new more hidden level that could not be touched by any retaliatory regulation. How could this happen? Does the legislation call out the NSA by name? If it does consider that maybe another agency is now doing it.