Site appears to be hacked

Seems like a very elaborate way to cheat.  If someone just wanted to win and was willing to cheat, why wouldn't they just use an engine? 

wtf are you talking about...

this sounds like the parinoid propiganda that has been floating around chess.com latley...

Sounds to me like you had one too much to drink. Remember, drinking can cause memory loss and loss of muscle control. Those combined produce the possibility of you moving without realizing it and forgetting it ever happened ^_^

Your mouse may be malfunctioning. This may also be the effect of glitches on the surface where you put your mouse. The laser which scans the surface sometimes recognizes those glitches as if you were actually moving your mouse.

I can observe sometimes mouse cursor moving randomly when I do not touch the mouse or computer waking up from standby "on its own" - when the mouse sends a signal that it was moved.

If you just tried to click somewhere but the cursor randomly moved towards your piece it might look for you as if the piece moved on its own

nice story bro!

Why would you just assume the entire site is hacked?  Are there dozen's of thread complaining?  Occam's Razor says you are more likely to have been hacked, or that your mouse is on the fritz ;).

People do this all the time.  The problem is usually a pebcak error.  Assume it's you until proven otherwise.