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That's not how I read it, when read in context. I would read it as "A player..." and assume something was lost in translation. It means you're allowed to do the same action twice to me. I don't think it's meant to limit that only a single player can do an action twice and prevent other players from doing that action twice.
Second this. Bus is a knife fight in a phone booth kind of game, but if each action was only able to be used by a single player, I'm pretty sure the game would fall apart.