We know about NSA & random wiretapping from the
misadventures of the previous tenant of the White House, that much is in public domain.
Without belaboring matters, let's say that I have a somewhat closer knowledge of NSA than most folks, enough to know that Wazoo is correct, they do not have "agents" like the FBI, DEA, etc. do. At least not that I know of.
I one spent an uncomfortable half-hour in an airport ticket line behind a loony who claimed to be an "NSA Agent," however, and he bragged that he had a "carry-my-handgun-anywhere" license that even applied in the FAA-controlled portions of the airport. Needless to say, anyone who really did have such powers is not likely to blab about them to random strangers in the airport.
Back in the day, employees of NSA were traditionally very reticent even to identify where they worked, beyond saying simply "The Department of Defense." Many people conjectured that NSA stood for "Never Say Anything."
Things have defrosted a bit ... near here at Ft. Meade, one can even find street signs that openly identify it as the HQ of NSA. Not to mention a very nice cryptography museum and a visitors center that sells T-shirts and golf hats.
-- rick