Two captains may not be put together for a revenue trip unless the captain in the right seat has been trained in the right seat—in addition to initial, transition, and upgrade training provided for that type aircraft. ("...maintain proficiency in each type aircraft and crewmember position...")

It's a fine point, but I don't believe you have to do ALL of recurrent in the right seat—contract aside. You merely, as a captain, have to be proficient in running things from the right seat (e.g. not climbing the sidewall while the other guy taxis).