I think mirroring is a direct WIFI link between your TV and the Miix and therefore can´t be connected to the router as well. While extending the Desktop it´s streaming the content via the router to your TV.
That sounds really strange, but not a bad idea.
Reading your comment I realised that there's another thing I forgot to mention. It's not that I absolutely cannot connect to the router, but frequently disconnects, and I cannot reconnect after that. So to be precise, there are small windows when I'm connected to the router while mirroring my screen.
This seems to make what you mentioned less likely.