I reread your first post and should have added that in my experience (CE/CW only) I was assigned a seat on BA for the CE section even when I did not have status. Might be due to flying J.
If I book a BA ticket on BA and AA metal (with my AAdvantage number) I can see part of the trip on AA.com. Somehow BA checks my AAdvantage number with AA and IIRC it is visible on the AA website as well, but it does not appear in my AAdvantage account summary until after the trip.
All in all it seems the systems talk with each other, but what you can see online is only part of the results.
I would call AA and check if everything is fine.