As others have noted, NSA isn't in Bethesda, and those mugs, along with keychains and tshirts, are available in the gift shop. Also, there's a 0% chance that the NSA would call him up afterwords to let him know that everything worked.
I'm sorry, but my post said things worked out - not that they cracked the code. I was clear they wouldn't tell me anything. I had always assumed the mug was from the gift shop. It would be hard to think otherwise.