One of the myths spread by Brodeur supporters is that the only reason that Curtis Joseph started in the Olympics in 2002 was that Pat Quinn was the head coach. In reality, Joseph was the consensus starter, described as the "frontrunner" for the position by CBC in November, and a pre-Olympics Slam.ca poll had 69% supporting Cujo for starting goalie, compared to just 15% for Brodeur. Joseph had been better than Brodeur in the years between Nagano and Salt Lake, and was also playing better in the 1997-98 season. He also had experience as a Team Canada starting goalie from the 1996 World Cup.
However, the way that Roy had been declared the starting goalie throughout in 1998 had not gone over well, and the coaching staff decided to change its tactics. Ed Belfour was named the 3rd goalie, and would not likely see playing time, but Brodeur and Cujo would be auditioning for the job during the Olympics. Cujo would play the first game against Sweden, Brodeur the second game, and they would go from there.
"Gretzky is so involved on this team that it's hard to determine exactly where his authority ends." (Source: CTV)
Pat Quinn was likely heavily influenced by Gretzky in all his decisions, especially concerning the starting goalies. It is unlikely that Quinn would have done something that Gretzky directly disagreed with. Most reports have the two agreeing on the plan to rotate the goalies until one of them shows themselves to be the #1.
Therefore, it was a management decision to share playing time between the goalies. Pat Quinn did not have the sole responsibility in naming Curtis Joseph as the starter for game one, and in any event it was not a choice that most people disagreed with. According to plan, Brodeur would see playing time in the tournament anyway.