I don't think this answer can be right. In a link battle, the player's Pokemon always comes out after the opponent's. So if 2 players named R and S sent out Groudon and Kyogre at the same time, then R's game would display, "Pokemon Trainer S sent out Kyogre! Go Groudon!" and S's game would display, "Pokemon Trainer R sent out Groudon! Go Kyogre!" If this answer was true, then R's game will say it's sunny and S's game will say it's raining, which I don't think can happen.