Yes, I agree with them. Just self study, borrow a few of the trial exams from the school, have a go at it and when you're ready, register with ASL (I think?!) and sit the exam. They will not care whether you did it with a particular school or studied yourself. The main thing is you pass the exam and CASA will hold it in their files. Then, CASA will give you a copy to show your chosen flying school you have done it so you can go for your PPL flight test down the track. Not much to it really.
But to answer your question, Of course it is transferable. It's inside your head - how can it not be. It's there wherever you go.