I'm here to second this. I was just in a game with some friends and someone who WASN'T controlling Mindskinner and attacking with a creature ended up preventing their damage and milling the table.
Whenever The Mindskinner is in play, any damage delt by any source to a player will be prevented and will mill the table. Even sources controlled by an opponent.
E.G. An opponent attacked another opponent, and it milled every player except the attacking player.