The Englishman's existence, though, will be acknowledged for a few days only. Parker's next fight has already been set, probably for early October, and next his opponent's identity will be revealed on Tuesday.
At which point, Joshua will again be off limits.
"If all goes well, that fight is still in the back of our heads," Parker said of his forthcoming trip to London. "But on Tuesday we announce a new opponent, and then it's going back in the vault."
That opponent, given it could be the last Parker faces before fighting for a world title, will likely be a reflection of the tall timber at the top of the division. Anthony Joshua has a height and reach advantage on Parker, and so do Deontay Wilder, Tyson Fury and Wladimir Klitschko.
The Kiwi needs to experience facing a bigger man and, alert to that, promoter Dean Lonergan hinted that Duco had arranged as a "hell of a test".
"He's a substantial unit, it's fair to say," Lonergan said of Parker's next opponent. "He's something we haven't faced before, and it's just another part of the road to the title."
The next section of that road will begin with a similar pre-fight plan to the one that conditioned Parker so well before clashing with Haumono: a couple of weeks' holiday, a shorter five-to-seven week camp is Las Vegas, before final preparations in New Zealand.
Parker believed there was still plenty to work on and said the message his knockout win sent to the boxing world was that he was always improving.
The 24-year-old's uppercut also illustrated yet another way he can win a fight, adding to an arsenal that could challenge any fighter. Whether it will challenge Joshua remains, for now, the tantalising question.
"We can't wait to get up to London and have our turn with Anthony Joshua, the man we couldn't mention last week," Lonergan said. "We just can't wait to get this heavyweight title shot going, because I think we're coming home with the title."
