I'd guess they could if they can guess your password.
is it possible that someone else could move my pieces in a rated online game?

Well maybe, but he made a bad move :)
Normally this go to a resign, but as far as i know in chess.com most players keep on and after this kind of moves, i dont know ...
Anyway some of them keep the ancient Greek «Εὖ ἀγωνίζεσθαι».
This means the idea of bringing together men and women to participate in a sporting competition based on the principles of brotherhood and fair play...
May i ask something please ...
I have participated in the tournament " World League 2011 R5: Romania vs Greece " and i play 2 games in Board 70I play in black in http://www.chess.com/echess/game.html?id=46908216
Suddenly i noticed that it had been a move 10...d5 that i m sure i did not play it ??
Is this possible that someone else made this move instead of me ?
Excuse me but i m sure i m not imaging things like this..
What should i do for my doubts?
Thanks