"That's not what rugby's about - it's about playing hard, then shaking hands afterwards. If you haven't got that, you might as well play soccer," he said.
Mr Heathwood said there was nothing wrong with rivalry, "but there's no need to cheer someone off injured".
He was accompanied by Janick Allamand from Switzerland, who was watching her first game of rugby, in what Mr Heathwood said was an example of the way the World Cup was opening up the game to a completely new audience.
Ms Allamand said she enjoyed the physicality of the game, the low level of commercialism compared with soccer, and the fact it was rough on the field but not off.
The world really did come to New Zealand for the Rugby World Cup finals, with hundreds of reporters from every corner of the rugby-playing world - and quite a few from places where the game is barely known. Friday night's bronze final was attended by 341 reporters and 151 photographers, most of them from newspaper sport departments.
The best represented countries were New Zealand, Australia, the UK, Japan and Argentina, with a large contingent from Uruguay and a smattering from nations such as Sweden, Hungary, Serbia, Hungary and China. The smallest country represented was the tiny European principality of Andorra, in the mountains between Spain and France, which fielded two reporters.
In a close fought match, Australia just headed off Wales 21-18 at Eden Park on Friday night to take out third place in the tournament.