If, as it was reputedly stated by the senior CC in question, she was too busy to bring these forms to the flight deck then it seems highly unlikely she would have time to note when she placed them under the door and note exactly when they were pulled in by FD crew.
It would help if we knew precisely what the CC did say/report, the 37 minutes could have been thrown in later by her colleagues or it could just be a guesstimate based on other events during the flight.