No, both are connected to the Sony. I switch video on the TV from Video 5 to Video 7, and it's HD on both. The 811 doesn't have a clue which TV input I'm using.
I don't use it on the other TV, because I don't know where to get DVI or component cables long enough to reach from the TV room to the bedroom.
The only reason I have two cables on one TV is because I wanted to see if there was a picture quality difference between the two, and I got a good price on a DVI cable at Sam's Club.