Someone at the NSA probably decided that since the existence of Los Alamos was well-known, they could safely allow some ex-employees to say they'd done secret work at Los Alamos.

Los Alamos the public was at least allowed to know existed. But it is not then obligatory to tell people you worked in intelligence, even if the joke depends on not being believed!

". . . a sort of Army liaison to the Office of Navel Contemplation . . ."