It is the old classified v covert ploy. If you can't get him on one, go for the other. Who told what to whom first. Crazy.
Heheheh. Except the "classified" one is meaningless mumbo jumbo with no legal ramifications whatsoever. IOW, you can't get him on the "classified agent" charge, because there is no such thing as a "classified agent."
When people outside the CIA know you work for the CIA, you are not "covert CIA."
I got a kick out of the "not widely know outside the intelligence community" throwaway line too. The intelligence community includes people from many many countries, most of whom are not covert agents.