World Rugby has referred the Scottish Rugby Union to its disciplinary committee over chief executive Mark Dodson's comments in the build-up to the World Cup game against Japan.
The match was in doubt due to Typhoon Hagibis and would have been cancelled, eliminating Scotland, if it hadn't taken place in Yokohama on Sunday.
Dodson had criticised World Rugby's "rigidity" and hinted at legal action.
The game went ahead and Scotland lost 28-21 to exit at the group stage.
At a press conference in Tokyo on Tuesday tournament director Alan Gilpin confirmed that the matter was now being handled by its disciplinary committee, adding "under tournament rules we're careful that people behave appropriately".
World Cup rules state that "where a pool match cannot be commenced on the day in which it is scheduled, it shall not be postponed to the following day and shall be considered as cancelled. In such situations, the result shall be allocated two points each and no score registered".
Dodson pushed for a postponement and claimed more effort would have been put in to ensuring the game went ahead if it involved New Zealand.
At the press conference Mr Gilpin praised tournament staff, some of whom slept at Yokohama stadium the night of the typhoon, so that match preparation work could begin as soon as it had passed.
He added that World Rugby had not yet started to count the cost of the three cancelled matches, which included England's pool game against France, the first time in the tournament's history that games have had to be cancelled.
Mr Gilpin admitted that there would be a financial cost, but added: "It doesn't change the fact that it was the right thing to do. The economic reality is something we'll look at when the tournament is finished."
When asked about the standard of refereeing, which World Rugby criticised at the start of the tournament in an unprecedented step, chairman Sir Bill Beaumont said that the refereeing "has improved" and that it was of a "good" standard.
There has been a record seven red cards issued so far at this World Cup and World Rugby chief executive Brett Gosper said the governing body was willing to "risk conversation and debate" as it drives "player welfare is the hard line to protect the players". He added that he believes there will be fewer red cards in the future as layers and coaches adapt to more stringent punishments for high tackles.