And what's the drawback of the input working when the XBox is on, if you can get the signal to pass through the XBox? Okay, so you have to issue a command to get the XBox to pass the video instead of outputting game video. This way you still only use one AVR input for two devices!
A good answer is easier with a clear question giving the make and model of everything. "The biggest problem in communication is the illusion that it has taken place." -- G. “Bernie” Shaw