It's possible for BA telephone agents to enter FQTVs towards specific airlines - while I was with BA I specifically requested (and got) the interface the agents use (Pegasus) to be designed that way.
IB flights can be credited to IB only and BA flights can be credited to BA only. Or vice versa. Or whatever combination you like. Ask the agent to specify IB to IB and BA to BA and while both FQTVs will be in the PNR and visible to both airlines, only the one appropriate to the airline specified will track.
Or retro claim if you prefer.