Anticipating the possibility of a 12-12 draw, the arrangement was that Charlie would leave the vote, go back to the Dolder Grand hotel and collect a briefcase left for him in the cloakroom. It contained US$250,000. A cab would rush him to the airport for the flight home.
After the vote Dempsey complained of "intolerable pressure" and later said this was in connection with attempts to bribe him. He and his family also received death threats.
There was at the time no evidence of Dempsey taking bribes but he soon resigned from the FIFA executive committee and as Oceania chairman.
In the end, it worked out for South Africa - they probably wouldn't have been ready in time to host the World Cup in 2006 and ended up hosting the 2010 tournament.
Dempsey's daughter Josephine King, who was the Oceania Football Confederation general secretary at the time of the infamous vote, declined to comment to the Herald last night.
"I don't wish to discuss anything about football," she said.
Former All White Bill Harris, who is also a member of Dempsey's lifelong club Eastern Suburbs AFC said he was shocked by the revelation.
"I would be horrified if it was true," he said. "It's hard to believe. Charlie Dempsey is held in very high regard in New Zealand and I'm sure people won't believe it.
"I'm kind of stunned - it's never come out before so it's a very strange and hard to believe allegation."
He said Dempsey had a very good reputation in the football community.
"In the few times that I met Mr Dempsey he was a great guy and very helpful to everyone."
Eastern Suburb AFC chairman Chris Ruffell said he did not believe the allegations.
Dempsey was the patron of the club for 20 years.
"I didn't know Charlie that well but I did meet him a number of times and I would absolutely flabbergasted if it was true. I don't believe it for a minute, he was a straight shooter in my opinion.
"He may have been a lot of things, but corrupt wasn't one of them."
Mr Ruffell said Dempsey would have "done what he thought was right at the time".
"What people forget is that South Africa have actually thanked Charlie for what he did because they admitted they were in no way ready to host a World Cup in 2006."