The relevant section of that document is
here:
AA Schedule Change
All American, American Eagle, American Connection Flights
American Airlines has a Schedule Change - AA Flights
...
91 minutes and greater
If no AA flights are available may select an alternate flight on AA* (AA codeshare) maintaining same inventory, origin/destination, fare and fare basis as originally ticketed.
Here, the original poster wants to take an AA* flight, AA codeshare on the BA morning flight. Same fare basis (award bucket) is indeed available.
This stated policy could form part of the original poster's argument against AA. AA's general tariff and prior statements to DOT (including when seeking antitrust immunity with BA) could also form part of his argument. Lots of sources of authority here.