Marketing drivel, pure and simple.
BA are pretty unlikely to be recruiting any low hours pilots in the next year or so, so the point is rather academic. What OATS won't have told you is that an awful lot more of their students have gone to Flybe and Ryanair than BA in recent times, and both of those airlines are happy to take candidates from modular backgrounds.
As already stated, BA only make the distinction for low-hours candidates - once you have 500hrs multi-crew time (their normal minimum requirement for direct entry pilots) where and how you got your licence is pretty much irrelevent.
This is not a clever time to be throwing £70k at an integrated course, and the schools know it - expect their marketing claims to get ever wilder and more desperate.