It said hotel arrangements are not made by the IRB, they are managed by tournament organiser Rugby NZ 2011.
It said "extensive discussions" had been held with Scottish team management about possible travel arrangements last week.
The Scottish Rugby Union, Rugby NZ 2011 and the IRB had agreed players would not pack their bags until they had either qualified or been eliminated, the statement said.
"As soon as Scotland gained a bonus point against England, it was confirmed to Scotland they would not have to leave their hotel until at least Monday.
"Once Argentina beat Georgia and qualified in second place, Scottish team management requested a number of team members leave last night rather than waiting for Monday or even Tuesday. This was requested by the team, not suggested by Rugby NZ 2011."
The remaining team members will relocate to an airport hotel today and will depart on flights to Scotland today and tomorrow, it said.
Rugby NZ 2011 said it had the full support of the Scottish team.
It provided a statement from Scotland team media manager Graham Law, who said Mr Bills' report was "totally inaccurate".
"The Scotland party wish to convey our sincere thanks to Rugby World Cup and Rugby NZ 2011 for all their support during the tournament and wish them every success for the remainder of the competition," he said.
"Furthermore we want to place on record our gratitude for the warmth of greeting we have received throughout New Zealand."