A lawyer for a Queensland family defamed by Alan Jones has expressed concern the Sydney broadcaster wants to slander them again.
Justice Peter Flanagan awarded Toowoomba's wealthy Wagner family $3.7 million - a record Australian defamation payout - after Jones unlawfully claimed they were responsible for 12 deaths in the Lockyer Valley floods.
Now Jones, his radio station 2GB's parent company Harbour Radio and Brisbane station 4BC are appealing an injunction in the judgment that was made against them in the Brisbane Supreme Court last September.
In the judgment, Justice Flanagan granted a request by the Wagners to stipulate Jones and the radio stations could never repeat statements defaming them.
In making the order, the judge noted that in giving evidence in the trial, Jones maintained the Wagers were responsible for the 2011 tragedy near Toowoomba.
That reasoning was disputed by Jones' barrister Robert Anderson QC in the Brisbane appeal court on Wednesday.
"The error, we say, in Justice Flanagan's approach was to both misapprehend and misapply the evidence that was relied upon," Mr Anderson said on Wednesday.
"It was entirely unfair characterisation of Mr Jones' evidence.
"Mr Jones did not say the plaintiffs were responsible or culpable for the deaths of 12 people at Grantham.
"That was put to Mr Jones, and he acquiesced."
Justice Flanagan found Jones and his co-defendants' defamatory comments were "extremely serious and of the gravest kind" and caused "profound personal hurt and harm to (the Wagners') reputations".
The family's barrister, Tom Blackburn SC, rejected any notion Jones needed to overturn the injunction to discuss the decision on air.
"The overwhelming inference, we would submit to the court, is that Mr Jones is intending or wants to, if the occasion arises, repeat one or more the defamatory imputations," Mr Blackburn said.
"One assumes he was advised by lawyers ... that he says an injunction prevents me and all staff ... from discussing most aspects of the decision.
"Well, your honour, it simply doesn't. It simply prevents Mr Jones from repeating the defamatory statements."
Mr Blackburn said Jones could discuss why he made the statements and "some the of background matters that affected my opinion when I made these broadcasts".
The appeal court judges reserved their decision.