A situational superko rule prohibits the repetition of the same situation.
Two examples of situational superko rules:
AGA Rules state: It is illegal to play in such a way as to recreate a previous board position from the game, with the same player to play.
New Zealand Rules state (reworded): It is illegal to play so that the resulting board position repeats the whole board position as it was after any of that player's previous moves.
Since New Zealand rules allow self-capture, the wording of their rule allows either player to play to create the empty board. AGA wording, plus self-capture would allow black, but not white to do so.
(Digression - A pass is a move in New Zealand Rules, so its not the same as Natural SSK)