Fulton, in so many ways the epitome of the hard-boiled professional who opened such a gap in standards between the two countries in the 1970s and 1980s, occupies an honorary, unpaid position. It is a surprising arrangement, but one which suits him perfectly.
'I have my own business and work that I do in the media and want to continue to do,' he said. 'It's a different situation from Malcolm Reilly in Britain, who does the job on a full-time basis.'
Fulton has just been reappointed until after a Kangaroo tour to Europe in 1994, so the arrangement must suit the Australian Rugby League as well.
A slightly better known but equally startling Fulton contradiction is that, distilled essence of Australia that he is, he was born in England, and of mining stock in Warrington at that.
'We emigrated because my father wanted to get away from the pit in Lancashire, but we moved to another coal-mining town in Woollongong.'
One of Fulton's main stocks in trade is a business that makes it unnecessary for him to draw a wage from rugby league. It is supplying chemicals to Australian coalmines, so he has a double reason for observing recent events in the British coal industry with interest.
'I don't know much about the politics of the situation, but if the position was reversed and we had the name of the company on our shirts like the Poms have British Coal on theirs, I would be tearing it off.' He sees little in England, nor has he done on half a dozen previous trips as player and coach, to make him regret his family's relocation. 'I sometimes wonder what would have happened if we had stayed in England. I might have finished up playing soccer.'
Instead, he became one of the legendary figures of Australian rugby league, moving from Woollongong to the Sydney club, Manly, at 16 and playing a key role, with his equal mix of craft and fierce competitiveness, in their first three premierships - two of them alongside Reilly - before ending his playing career with Eastern Suburbs.
Given an almost familial relationship with Ken Arthurson, the most powerful man in the game in Australia, it was long regarded as inevitable that Fulton would eventually graduate from coaching Manly to coaching the national side. His record since assuming that role in 1989 is not without blemish, however.
Australian sides coached by Fulton have gone one-down in series against Great Britain and New Zealand as well as needing a third and deciding Test to beat off the British challenge this summer. There have been criticisms of his team selection, his match preparation, his eagerness to be one of the boys.
His record also shows that he has a knack of getting it right in the end - Australia won all three of those series - but in a World Cup final there are no second chances. 'In 10 matches against Great Britain, we like to think we would win six and they would win four - that's about the balance between the teams now,' Fulton said, 'but this could be one of the four.'
Not that he lacks confidence; he knows that he has a well-balanced team who have enjoyed a gentle preparation perfectly geared to their needs.
But he has changed his tone subtly from the summer when, despite an embarrassingly heavy defeat in the second Test in Melbourne, he remained unshaken in his belief that the extra power of the side he had chosen would see them come good in the end.
Now he plays down the difference in size and strength. He knows the weights of the British forwards and reels them off, occasionally adding a few English pounds or Australian kilogrammes for effect.
Players like Ward, Platt, Betts - Britain has plenty of power these days as well. That is not the difference any more. The difference is, he suggests, one which many in Britain believe operates in precisely the opposite direction, but he is adamant that the stricter policing of the offside rule in Australia gives his players more chance to play open rugby. 'I'm fortunate that so many of the players in the Australian team now come from clubs like the Brisbane Broncos, where the whole philosophy is to do that.
'I'm not exactly the same in my approach as club coaches like Wayne Bennett at Brisbane or Tim Sheens at Canberra, but there is the similarity in that, if the chance is there, we will move it wide. That makes it easy for players to slot in.'
The trend for defences to sneak up and stifle ball movement is still British rugby league's main problem, he believes. He has been outspoken about British refereeing standards in the past; a BBC interviewer still bears the scars of a lively discussion on that subject after the tour match at Wakefield two years ago. Fulton went on the attack so outrageously that the interview was played for laughs between records on Radio 1.
The impression now is that he has mellowed considerably. He did not put up the fight against the financial imperative of conceding home advantage for tomorrow's final at Wembley that might have been expected from a man with such a famous hatred of losing. 'It's a much bigger occasion in Britain than it would be in Australia,' he said. 'It's good for the game of rugby league that it should be here.'