It has been confirmed that some mobile basebands are, in fact, remotely controllable even when a device is apparently off. It isn't a far-fetched scenario.

http://www.seattletimes.com/nation-world/even-if-theyre-off-...

In this case it was a Motorola device on an iDEN network, probably using a Freescale baseband. But it is likely that most major vendors were persuaded to include similar capabilities and that network providers cooperate in providing special signaling to control these capabilities.