As a challenger of Klitschko's on that remarkable night in Germany last November, Fury, who hasn't fought since so has yet to get the big payday that he deserved as champion.
And, after unlocking the seemingly invincible Klitschko's hold on the division with a smart performance over 12 rounds, few would deny he deserved that.
Professional boxing is full of stories of those who failed to take their opportunities for one reason or another.
Parker was eight years old when fellow Kiwi-Samoan David Tua fought Lennox Lewis in Las Vegas in 2000. Lewis was far too good that night but Tua, a knockout specialist, turned up in less than ideal physical condition and hardly fired a shot.
Kevin Barry, Tua's trainer and now the main man in Parker's corner, is determined that this story has a different ending. Parker's dedication to constant improvement gives him an advantage, as does the fact that the heavyweight division is so splintered and in a state of flux.
Parker is the mandatory challenger to Anthony Joshua's IBF title - which he will probably fight for in November should he get past Alexander Dimitrenko in Manukau on Saturday - plus he is ranked No1 beneath Fury with the WBO. Deontay Wilder is the WBC champion, so there's another route for Parker should he need or want it.
But while the lessons of Tua's career will remain fresh and relevant due to Barry's experiences, there is nothing like watching significant events in your sport being played out when you are in the middle of it all.
One can only imagine the pressures on boxers as they prepare to get in the ring with so much at stake. Some are clearly better at it than others. Fury is an over-thinker according to his uncle Peter. Muhammad Ali used to sing, dance and tell jokes in his dressing room before fights, and Parker shares the same traits according to his promoter Dean Lonergan.
"Considering the intense environment that he works in - and that is the world of heavyweight boxing - he would be the most relaxed athlete I've ever seen," Lonergan said. "I've seen guys go into dressing rooms before rugby league matches and rugby union matches and want to tear down walls and headbutt them, but Joseph Parker comes out and wants to dance.
"It's quite incredible seeing how relaxed he is, but one thing he's never had is the potential of a world title fight on the line which he has now, and he has to concentrate on Dimitrenko, otherwise all this talk of a title fight goes out the window."