It was terrifying enough for me in the gig I worked on that dealt with reservations and check-in, where a catastrophic failure would be someone boarding a flight when they shouldn't have. To avoid that sort of failure, the system mostly just gave up and issued the passenger what's called an "Airport Service Document": effectively a record that shows the passenger as having a seat on the flight, but unable to check-in. This allows the passenger to go to the airport and talk to an agent at the check-in desk. At that point, yes, a person gets involved, and a good agent can usually work out the problem and get the passenger on their flight, but of course that takes time.

If you've ever been a the airline desk waiting to check-in and an agent spends 10 minutes working with a passenger (passengers), it's because they got an ASD and the agent has to screw around directly in the the user-hostile SABRE interface to fix the reservation.