"They told us to face off, then told us to split," Parker said afterwards. "He wouldn't move and then I wouldn't move either. They said 'move', and I thought 'he's not moving, I'm not moving, I'm staying here'. I don't know if that's winning or not. He backed away. He seemed real angry, like seriously angry - I could feel it.
"Being angry before a fight – I don't know if that's the best way to approach a fight. That's tension that you shouldn't be wasting on being angry or upset. If he's angry, then let him continue to be angry - I hope he gets angrier."
Asked if that could make Joshua, the IBF and WBA world heavyweight champion, more dangerous at the Principality Stadium, Parker said: "I think it will make him dangerous but it won't be controlled. If comes in on the attack he won't be thinking as clearly if he's angry. I'm cold-blooded. Everything's thought about in my head properly.
"He didn't even look at me when I looked over at him [during the press conference].
"We've been pretty victorious outside the ring - now we have to be victorious in it."
Whether any of this makes a jot of difference during their world heavyweight title unification fight obviously remains to be seen.
But Parker, giving off a Clark Kent vibe in his grey checked three-piece suit and (non-prescription) spectacles, appeared to enjoy himself at least. He smiled and nodded his head in time to the music at the top table as Joshua made his way to the front.
Later, standing and holding an apple and a glass of water, Parker spoke to the many media hoping to get their own time with him. This he did with humour and respect as he has for the past 10 days or so in London.
During the press conference there was a veneer of respect from both sides after Higgins attempted to set the agenda with a warning for Hearn not to try to goad him and that it was time for the fighters to talk.
Parker said afterwards of Joshua: "He hasn't said much. He's been relying on his promoter Eddie Hearn to talk for him. It's good that David put him on the spot today."
Joshua's trainer Rob McCracken came closest to the edge as far as his team was concerned, when, after a bit of banter between Hearn and Higgins, he said Wladmir Klitschko, whom Joshua knocked out 11 months ago, was a bigger challenge than the 26-year-old Kiwi.
McCracken added: "Being fast, being calm and collected – all the things you need going into fight night, it doesn't prepare you for getting in the ring with Anthony Joshua, it really doesn't. It's not just the size of him – he's very imposing in the ring. He hits you and you don't know why you're getting hit."
Joshua, who brought up the issue of what has been described as a "snubbing" of the New Zealand media, said in a cryptic way that he would knock out Parker.
"People think I walked out on the New Zealand, what are they? Press people," Joshua said. "But that wasn't the case as such. It was because I was there from 10am in the morning until 5 and I had to get back into the gym at 6.30 to train. It wouldn't have mattered if it was the African press, the Chinese press or the Russian press, or New Zealand press."
For his part, Parker, scheduled to travel to Cardiff straight after his media commitments, said: "I'm going to beat him. I haven't decided how I want to beat him yet – whether it's a knockout, points, or decision, I'll see how I feel on fight night."
