Just to add to the above,and answer your other question, yes BA book the Basic (HBO) and Plus (Cheapest checked bag inclusive fare) into the same booking class. All you're doing effectively is picking one branded fare with different inclusions over another.

You're right in the sense if purchasing a BA flight number as opposed to a IB flight number then BA rules apply. BA HBO fare = no OWE exceptions to the checked bag rule and no checked bags are included. Pay extra for the Plus fare, have 1x23kg checked bag included then this bumps up to 2x 32kg checked bags because of your OWE status.