WBA, IBF and IBO heavyweight champion Joshua and WBO belt-holder Parker are set for a unification bout at Cardiff's Principality Stadium on March 31 in a hotly anticipated clash.
In November, before the fight had been agreed, the Parker camp released a video which showed Joshua being knocked down during his amateur days, as well as clips from former sparring partners claiming they had floored him.
At a media conference on Tuesday, Parker's promoter David Higgins spoke up about the issue.
"In most countries in the world it's customary in sport to analyse the strengths and weaknesses of each opponent," he said. "Something that shocked us is apparently in English boxing it's not customary to do that.
"There seems to be shock that we dare speak about things. Joshua has allegedly, in the footage going around, been dropped a few times."
— Matchroom Boxing (@MatchroomBoxing) January 16, 2018
Joshua was quick to cut in on Higgins in an attempt to clarify the situation, explaining he had only been sent sprawling three times - in the European championships, in sparring by David Price and in his epic win over Wladimir Klitschko last April.
"You know what I learnt when I got dropped in that Klitschko fight?" he said.
"The three times I've been hurt or dropped were in the European championships when I was unfit, the second time was with David Price - he's a puncher.
"It [Klitschko] taught me, it will take more than a human to stop me from where I'm destined to be. The rumours you've heard, it's fake news.
"I think the trash talking should still hold a sense of respect. There are two types of people who take a punch, one who gets put down and stays down and one who gets up and keeps coming, and that's who he's facing."
Photo Getty Images. Caption: Anthony Joshua and Joseph Parker