So you're on an AA (001) ticket and an AA flight number?

AA, BA, IB and AY all treat allowances for status passengers under Basic Economy tickets differently, so the detail will likely be important here.

But in terms of BA exercising discretion in allowing more than whatever your checked baggage allowance is, on long- haul - where generally there's plenty of space in the overheads - that's certainly not something you should expect to happen.