Just got off the phone with BA regarding a schedule change. Over the course of our call, the agent mentioned I do not get a free 2nd checked bag. Huh?? I'm in ET into LHR, connecting to an AA flight (in Y) back to the States. Doesn't the most generous of all carriers' luggage restrictions apply? AA gives Aadvantage Gold members two free checked bags on transatlantic journeys.

Am I, or the BA phone agent in the wrong here?

Thanks.