Defined in law
Up to 1999 the law said "He cannot alter a decision unless he observes that a touch judge's flag is raised or before he has received a report from either or both of his touch judges relating to Section 4 (a).."
In the 2000 rewrite this was changed to "The referee may alter a decision when a touch judge has raised the flag to signal touch or an act of foul play " which seems to leave open the possibility that he can also change it at other times.