It doesn't matter - if the Authorities don't care then what's the point in fretting about it.
The entire industry is just "smoke and mirrors" - it just needs to "look" good.
But (shouldn't start a sentence with "But"), if all the exams are done, then all the flying is done afterwards, it cannot be an INTEGRATED course. Can it?
The course is done in modules - ground, then PPL equivalent, then hour building equivalent, then CPL equivalent, then IR equivalent.....and the "progress tests" underline that.
It's modular - you just do it all at one school, wear the same uniform and pay twice as much. But it's modular by definition of what an "integrated" course is supposed to be (and used to be).
(I did it again).