"But was she really a secretary or just someone in the typing pool at the base?"
According to Killian's son, she was in a pool of secretaries who did typing for many officers around the base. In addition, why should Killian confide his personal feelings about another officer to one of the secretaries in the pool? This would have been a no-no, and to all accounts, Killian was a very honorable man.
So it seems if we could prove this point based on personnel records from the base, that would pretty much expose her as a fraud.