I don't work for BA, so my information is third-hand, but as I understand it the reasons are historical. In the olden days before JAA, when the choice was CAP509 (what is now integrated) or the self-improver (modular) route, BA allegedly took on a few low-houred self-improvers, and weren't particularly impressed. Since then, all recruitment of inexperienced pilots has been via the 'approved' / CAP509 / integrated route. Presumably a candidate from CTC would be acceptable as they have passed an initial selection and would come with a verifiable training history (the CTC course being integrated in all but name).
Note that once you have enough commercial experience to apply to BA as a direct entry (experienced) pilot, they are as disinterested as everyone else as to how and where you got your licence.