As a former AA employee, I'm absolutely sure the AA agents communicated with BA's agents at LAX. AA would give BA the estimated arrival time of the flight. It seems to me that it would then be at BA's discretion of whether to hold for the connecting passengers. This type of issue can and does happen everyday at LAX and other hubs. It is something that the AA and BA employees handle on a daily basis.
It sure would be nice for an AA or BA agent at LAX to chime in here. I'm sure that there are all sorts of considerations.