Joshua - promoted by Hearn and Matchroom Boxing - defeated IBF mandatory challenger Kubrat Pulev to remain on course for an undisputed clash against Fury.
AJ possesses the WBA, IBF and WBO belts while his compatriot currently holds the WBC and Ring Magazine titles as well as the prestige status of being lineal champion.
A two-fight deal was agreed in principle by both camps for 2021 but a sticking point appears to be Oleksandr Usyk, the mandatory challenger for Joshua's WBO title.
Despite the threat of blocking an all-British unification battle, Hearn is adamant Joshua vs Fury will go ahead with or without the WBO strap.
"We have a fight on our hands; I'm sorry for the governing bodies, [the fight] eclipses all belts.
"We've just got to be a little bit careful because you may be on the verge of; you know what? Let's just get rid of politics right now.
"Let's just drop all the belts because if we lose one belt [the WBO], we might as well lose them all."The WBO expects Joshua to face Usyk next unless the Ukrainian accepts a substantial figure to 'step aside' or the belt is vacated.
Hearn added: "So, it gets to the stage where you've got the biggest fight [Joshua vs. Fury] in world boxing, you're paying each governing body hundreds of thousands of dollars.
"Now you've got another guy [Usyk], who probably wants seven figures. We've just got to be careful because the ultimate aim of this fight has always been to be for the undisputed championship.
"When Anthony Joshua came into my office many years ago, that was always the dream, and we will do whatever we can to make sure that every belt in boxing is on the line for the Tyson Fury fight.
"What we don't do is we won't be held for ransom, and we won't let politics get involved in a fight that boxing needs."
The WBO remain firm on their mandatory status
The WBO does not appear willing to waver from their position. Soon after comments from Hearn, the organization's president Paco Valcarel reminded the promoter that he 'knows the meaning of commitment'.
Hearn clearly went on this tirade to try to put the governing body under pressure to allow Fury vs Joshua to happen.
Not only will Joshua vs Fury be more entertaining, it will be more lucrative for all involved as well as becoming a historic moment in boxing history, something which may entice the WBO.
This level of a fight is what is needed if the sport is to continue to grow during difficult times in the pandemic according to Hearn.
With both camps craving the fight, fans will feel half full rather than half empty about the chances of the showdown happening in 2021.
However, Usyk is part of the Matchroom umbrella and should Joshua vacate the title, it could see the 2012 Olympic champion cross swords with "Juggernaut" Joe Joyce - an opponent he knows too well from the amateur circuit - for a version of the heavyweight world championship.
By the end of 2021, boxing should know the best heavyweight on the planet but on second thoughts, let's say 2022 to be on the safe side.