You are reading too much into it. BA have used every Integrated school (there only ever were 4) there has ever been. They periodically moved the contract about and dipped their toes in other schools waters.
OATS did get the bulk of BA cadets from the later 90's. But many said they were welcome to it - such was the discount that many believe no profit was made doing the training. Mind you - as a recruiting tool for more lucrative business it was a priceless contract.
There basically is NO difference between any of the large schools and to be honest the deal at smaller school is often better in my opinion. BA couldn't tell the difference between someone trained at Kiddlington, Jerez, Cranfield or Little-Piddlington-In-The-Marsh. And neither can anyone else.
Cheers
WWW