Okay, the circumstances were a bit dodgy, but my TiVo rebooted all by itself. Unfortunately, I wasn't watching video from the TiVo when it did it.
Basically: (1) I pressed the power button once to turn it off, and got the usual dialogue box telling me it would power off in a few seconds, (2) I switched my TV's source to its internal TV tuner, (3) I remembered something else I wanted to do with the TiVo, so I pressed 1 to stop it powering off - and it went into the restart cycle!!
I've cancelled a TiVo shutdown without being able to see the power dialogue before, and it's worked fine. I really don't know what happened this time. Surely it should have asked me to do that thumbs down last channel thing before it can reboot. I was grateful to find that it had only rebooted and not done a factory reset!
When it happened I was panicking that it was doing a full factory reset and losing my recordings. I thought that I'd somehow hit on a magic key shortcut that resets the box. I've been unable to reproduce this behaviour, so maybe it was down to timing. I definitely pressed the numeric '1' button as it was counting down to standby.