Same thing happened to me once in MIA as well

A regular agent on a BAEC phone line is like to say no (given the time of day).OW association between AA and BA accounts for nothing.

Thankfully, I remembered to phone the phone down and called the Gold line in London, got an experienced and more generous agent who managed to put us on the flight on the next day. I know that was a one off and not standard practice.

Its one of the hidden benefits of being Gold that is never published as it is discretionary.