I don't believe that this is BA who do it but the IFE company that supply BA. There is normally more than one pop up of the airline name during the film. The timing of the name check in the film in this case is rather good though given Daniel Craig is on a plane at the time. The same is done by the distributor/studio for edits to films where there may be distressing content (1), or another airline(2)

1: An example would be The Sentinel where the marine helicopter leaving Camp David supposedly carrying the President is shot down by a SAM* which has the potential to affect nervous flyers.
2: An example would be Casino Royal and the removal of Virgin and Sir Richard Beard (which happened on multiple airlines not just BA despite what you may have read in the papers).

*Surface to Air Missile