In the mission where you go to the boat loaded to leave the island if your partner skips through the cut scene the enemy attacks immediately leaving the other player still in the cut scene. All players need to exit the cut scene before the attack starts.
There was a game which had this (mandatory) feature, I can't remember which one honestly.
All players MUST decide to skip the video, otherwise if not all, the scene simply keeps playing until its end. To highlight that other players are asking to skip the scene, a message should appear somewhere on the screen.