I haven't come across this myself and I have to admit to never having paid any real attention to the stated baggage allowance on my BA-ticketed QF domestic itineraries. But from first principles, one guess (I stress it's no more than a guess) is that BA has wrongly written a 40-kg (ie weight-based business class) baggage allowance on the ticket, which is what the QF website is picking up and showing you as your included baggage allowance, even though it ought to be a piece-based allowance. But then when you ask QF for more baggage allowance, then as that is a purely QF function, the QF website is accurately identifying that it should be offering you a piece-based additional baggage allowance.

One way of testing that is to get a copy of an Amadeus-generated e-ticket receipt that actually shows the ticketed baggage allowance on each sector. Unfortunately, I'm not sure that CheckMyTrip does that in either version - can anyone confirm?