I remember reading about this at the time. Can't really work out why AVB leaving to manage a club would mean him falling out with Mourinho. As Mourinho did exactly the same thing himself when starting out.
Perhaps due to the ageing players at Inter, Jose was simply protecting AVB from getting involved in something very similar to Chelsea. Or maybe due to his relationship with Levy he thought - I will make sure AVB gets back involved in a club that suits him perfectly