Does the tv have one of those HDMI ports that allows funciton control? I forget the actual temr, but I know my tv allows "HDMI device control" or some crap.
perhaps this type of port always has some sort of power, even when display is off.
An easy way to check, is to simply unplug the tv power cable, and see if the computer now sees it as off or disconnected.
Apologies if my wording is off, I am being aided by some Fireball whiskey.