Higgins, angered by the decision to appoint British referee Terry O'Connor for the fight at the Manchester Arena, approached Hughie and Peter Fury and the fight promoter Mick Hennessy and made an allegation which Peter responded to by saying: "All you've been doing is squealing. Squealing like a pig."
Peter Fury added: "You're rattled.
"Who gives a ***k about you anyway?"
Higgins, on his way out of the room due to the efforts of a towering bouncer, said: "You shook my hand. Neutral refs."
Hennessy, who said he had nothing to do with the appointment of the referee, later questioned whether Higgins had been drinking.
Peter Fury said: "I do apologise for my language but it's not nice to hear your promoter saying Higgins has threatened to pull out of the fight, saying 'you've breached' and he wants to run away with the money.
"You're hear all this rubbish talk and he comes in here and says 'what about the referee?'.
He said he would be happy for Parker to check and approve the gloves, ring and dressing room. That's what I can do for fair play. I want my son to win a world title with no hidden agendas. Now, Higgins is basically saying because of the referee it's not fair. He's insinuating I've got the [British] Boxing Board of control, one of the most respected officiating groups in world boxing to say I've got them in my pocket, they're bent. I've got no interest in a referee, a judge or anything else.
"All this stupid, silly nonsense... I'm not interested in all that crap."
Parker told the Herald that Higgins' antics were all part of the sport of boxing.
"It's part of boxing. The fight doesn't have a lot of interest so let's do something to make it have more interest so people are aware we are fighting," he told the Herald.
Parker's trainer Kevin Barry said: "Look, I can understand David Higgins' frustration. He's our promoter and responsible for the contract we have in place and I know there are some things in that contract ... like neutral officials.
"Let me say to Peter, please don't worry about David running off with the money because we're going nowhere. This is an opportunity...
"We've waited a long time, and not just for Hughie because this fight has been backwards and forwards for six months, but we've waited a long time to campaign in the UK. The timing for us is perfect right now.
"Right now I believe he [Parker] is at his best."
The fighting talk, thankfully, wasn't confined to promoters and trainers, with both boxers saying they were confident of a knockout victory.
Fury said: "I'm going to knock him out. I've trained for it, I've had super sparring. I think I'm going to knock him out."
Parker replied: "Same here, I'm not sure what round I'll do it - somewhere between one and 12, and then we're going to get up and be gentlemen and friends after the fight."
