Yep - Braniff crews trained to fly the full envelope. But for BA insurance reasons, there had to be a BA captain and flight engineer riding along in the jumpseats.
Another cute trick - the European airlines "sold" the airframes temporarily to Braniff, with new US N-numbers, so they could fly a "domestic" route without violating cabotage laws. Then "sold back" to BA or AF for the transatlantic legs.
CONCORDE SST : Braniff Concorde Services