That is wrong, BoeingBus.
I had an application form from Citiexpress, which they would not send me until they had checked I had been on an approved course. All JAA courses are approved. The form itself also specified either an approved course or a CAA non-approved modular course and 1000 hours.
The split between modular and integrated is a memory of CAA times, when modular courses were not approved: both now have the same status, one of the few good things to come out of JAA.