I wonder if you could have checked in on the phone, by providing the agent your two PNRs. Once checked in you'd have a BP on your phone to get through TSA and to the gate, or "re-print" from kiosk.
If not checking bags, I would have tried this.
As others have noted not IDB. but no one has explained the reason, which is VDB/IDB rules and compensation were put in place by the gov't to provide an incentive for airlines to be more conservative when overbooking. They weren't put in place to provide compensation for random customer service failures like this one. That's why you get situations that seem silly from the outside, like that there is no penalty for cancelling a flight outright but they pay thousands of dollars per overbooked cust for an equipment swap. Or, in this case, no penalty for (essentially) refusing at random to check people in.