I've had this problem for the past few months. I'm on an early 2009 iMac and a third generation ATV, running Mavericks since a few months ago. I can't remember whether this started happening before I upgraded to Mavericks, but I think it did.
The solution above did stop the ATV remote from opening iTunes if it's closed, which lets me use the ATV in peace after I close iTunes. That's great, but I like to listen to tunes using the Remote app in the bedroom while I get going in the morning, so I'd prefer to leave iTunes running so I don't have to remember to start it back up before I go to bed.
However, no combination or sequence of pairing, unpairing, and turning the iMac's IR receiver on or off stops the ATV from controlling iTunes. And, in case it matters, the iMac remote continues to control both the iMac and the ATV. It seems that the IR receiver is working, so I don't see a hardware glitch.
So, considering that the ordinary solution didn't work, does anyone have another way to stop the ATV from controlling iTunes while I'm using the ATV?