I really haven't followed the story closely, but IIRC, her so-called "cover" was blown in that "heavy make-out session" with her future spouse.
I've had numerous conversations (long ago) with individuals who had knowledge of CIA personnel and operations. There is NO WAY IN HELL they let anybody (including close friends) know they worked for the agency. When asked about where they worked, they used the title of some harmless, nondescript agency.
You are correct.