So I have the same symptoms but I cannot get my ATV to show up in iTunes on two different machines.
I followed the instructions in this thread (and the other), as well as from this Article (http://support.apple.com/kb/ht4367) and still no dice.
Should I just leave it plugged in for a few days and see if it auto fixes itself? Not much else I can try at the moment. Can't very well restore if I can't even see the ATV in iTunes (MBP And Mac Pro, both fully updated with iTunes 11.1).
I stand corrected!
Just did a iTunes restore on my (already on iOS 6) aTV 3 and this time around it indeed required the power plug to enter recovery mode.
I wonder if it was changed somewhere along the iOS releases?