The Stena Clyde drilling unit was operating under lease to Origin Energy when an incident on the drill floor killed two men.
But it says it was only allowed on site after it pursued right of entry through Fair Work Australia and drill owner Stena reversed its decision to not allow them on board.
MUA assistant national secretary Ian Bray said the union was calling on federal Resources Minister Martin Ferguson to amend the legislation to save all parties the difficulty of continuous disputes over right of entry.