I can't recommend enough to read the book "Command and Control: Nuclear Weapons, the Damascus Accident, and the Illusion of Safety" by Eric Schlosser. You will be surprised how often we barely escaped nuclear war because wise people chose to not trust the machines.
Did the gate agent do any follow up verification? Like checking the flagged passenger's ID?
In retrospect, modern computer systems are inscrutable and unreliable enough (as a category) that it's rational to disregard them, especially if you've done some independent verification. Rational doesn't always mean correct in a specific case.
1. Computer says no, leading to the true passenger being rejected. Probably would have resulted in the guy managing to steal her seat and maybe not getting caught.
2. Computer says no, overreact, and reconcile everything until the computer is satisfied (e.g. deplane everyone and start over, maybe checking IDs). I'd guess this attitude would result in hundreds or thousands of delayed flights when everything was fine.