The details on complicated. Most instances where a pilot has an entitlement to a FC/BC seat only apply if a seat is available at the time the deadhead is scheduled. No rights to bump a passenger if FC/BC is already full.

Was formergr's flight a long-haul (>8hrs I think) international flight? That is the only time that I can think of that a DHing pilot has an entitlement to the seat even if FC/BC is full.

Just guessing from the information presented, the DH may have been booked in FC/BC but the pilot was late and the GA was in the process of releasing his seat when he showed up. He could have been late due to a tight inbound connection, tight hotel transportation (they schedule it tight!), or being a late call-out from reserve.