An actor should only move a set piece if they have ALWAYS moved that set piece. A director I've worked with said he was doing tech work for a production of "The King and I" and his job was to set a prop on the stage, and then go off and pull a drop. Well, one of the people backstage tried to be helpful, so they pulled the drop and the lights came up on the King's funeral and in the middle of it all was some guy in black pants and black shirt.
During a dress rehearsal for a production of "Big: the Musical" I was in, one of the techies was supposed to push off a carnival game table during the transition to the Zoltar machine. She was about to when two of the actresses in the scene took the table and rushed off with it. We found out during our break that they had run into the backdrop and ripped it, costing us almost $1000 in damages. After that, six actors were assigned three tables and from then on only those six were allowed to move the tables off.
So, unless someone has done something at every rehersal and the director has told them to, they should NOT do it.
-- SDG