Another data point. AA EXP flying AA but booked via BA and with a BA ticket number. Bags were checked in for free without any question, though strictly speaking I think it wasn't an entitlement due to the BA ticket number. The first flights were a domestic leg then connecting to transatlantic so the first agent was only used to dealing with AA domestic where AA elites do get bags. I wondered if the computer would flag up the zero entitlement though, as BA's computer does, but now we know.
(The return leg was direct on BA and I had to pay for bags, which I was prepared for.)