Can a Special Event be used to help another player during their turn?
Yes, you can play special events on other players' turns, and "current player" means the player whose turn it currently is. The rulebook says:


  These cards may be played at any time (even on a fellow player's turn)...


That's why they say "current player" not "you", and explicitly say you can play them any time, not just on your turn. Being able to use them to benefit any player is really the point. They'd be pretty weak without that flexibility.