I'll bet this is some kind of a ground loop going through the tuner. Your player is getting its ground through the antenna wire connected to the tuner instead of getting its ground from the ground wire on the sled.
Quite possible. All I know is that the installer did some funky wiring. I noticed a few wires were cut that I didn't think should be cut.

The only way I can see that your player is getting random button presses is if there's noise on the serial
oooh, I hadn't thought of that. I'll check to make sure that the dust cap is still on the serial connector.
and/or stalk inputs.
This was my first guess.
I haven't scrolled back in the thread, but did you try disabling the stalk in the player configuration?
No, I didn't think about that, as I thought it was a hijack feature, which I don't have installed. On top of that, as luck would have it, my Java installation is currently fubar, so I can't check it out in JEmplode.