Well, it's all a big company play, isn't it? - with a dozen companies and subsidiaries that are still all owned by Qantas, when it comes to the crunch?
Cobham (formerly National Jet, to those who came in late, as the Phantom says) talk of "providing services" to QantasLink and Australian Air Express - but Qantas still owns them all.
Technically, you're correct, but it's all a big paperwork exercise designed to minimise tax and gain other financial "arms length" advantages.