I have always had full MMB functionality when codesharing on other airlines metal/flights and not had this sort of problem before.
Just because you've had full MMB functionality when codesharing on other combinations, it doesn't mean it will be the same for this BA/QF combination or anything other combination out there. If BA has placed a restriction on what services you can access when flying on QF metal with BA number/stock then there's nothing you can do about it but suck it up and accept that BA is the limiting factor. That being said, you should at least try and get to the bottom of the issue to learn and not have the same issue again. If QF has passed the buck onto BA, contact BA and confirm.