This story breaks down, and raises concerns, at the same time.
Breakdown: If the 13yo was a UM, she should have had an adult with her through the security process at the departing city (adult would be an NPE... Non Passenger Escort), all the way to the adult hand-off to the FA. So there should have been no lack of awareness by an adult at the CP, or at the gate, for a UM.
Concerns: if the 13yo was not a UM, the check-in agent could have refused an NPE to the adult, and the adult could only have gone as far as the TDC. Then the 13yo would have been on her own, at the potential pat-downs at the CP, or the gate. Also, if there was a connection, even if travellng as a UM, there could have been a gate pat-down, which no adult would have had an option to walk the 13yo away from.
The issue is, a minor, specifically a young-minor, has no representation at a good portion of the security process. It's not like a 13yo can get to the gate at a connecting city, refuse the gate pat-down, be escorted out of the airport, and told "go rent a car, and drive home".