I think this is a gate agent just buying time. Taxiing anywhere around ORD should not take more than 15 minutes to 20 minutes total. Even with bad weather and planes stacked up for takeoffs, there are plenty of taxiways to get around O'hare.

The AA hangers are near the United hangers on the NW side of the airport. The only active runway they would likely have to cross is 9L, which is usually used for departures but is occasionally used for arrivals. If it were being used for departures, they would have been able to taxi on T without disrupting the flow.

I am guessing it just took the crew longer to get the plane out of the hanger than they thought.