Originally Posted by KARFA

That sounds very odd. There really shouldn't be any issue rerouting you on AA to the nearest place with BA or AA flights still running to LHR. Any joint business routing which includes AA should be fine if you are sticking to same dates or no more than -3/+14 days from the original. This is all available under the standard guidelines for cancelled BA flights option 3. You do not need reward availability on your new flights, just any space in the cabin is sufficient - if you were going beyond -3/+14 days they would seen reward availability on any AA flights.

I think this may be a case of hang up and call again.