It's not IDB; but it's unacceptable for UA to refuse to check them in when they were at the counter 10min prior to cut-off. This is much more deserving of a scandal than the incident with a cry-baby doctor who refused to give up his seat.
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KPhill I hope you are compensated accordingly and the agents involved are disciplined severely.
For an example of how an airline _should_ handle this; I was recently flying EK F SFO-DXB and showed up at 12:30 for a checkin counter that opened at 1:15. They couldn't check me in and I had a business meeting at the Centurion lounge. Proceeded to book a refundable domestic ticket to get through security and get my meeting done. I lost track of time a bit and at T-65 I get a phone call from the check-in agent asking me where I was. Told her I was in the terminal and would be right there, and she processed my check-in at T-55 about 5min _after_ cut-off. This is how you provide top notch service. (No bags to check for me; couldn't do online check-in because of my passport.)