The Dominion Post reports the recording shows neither Ms Pullar nor Michelle Boag, who supported Ms Pullar at the meeting, made the threat to go to the media.
It also found ACC's claim that it was not given specific details of the breach was misleading, as the managers at the meeting were told it contained the details of 6,500 clients and "highly sensitive information".
ACC's claims were detailed by the Corporation in a report ordered by ACC Minister Judith Collins. However the ACC has refused to the amend its report, despite being given the recording three weeks ago, the Dominion Post reported.
The report was published without Ms Pullar or Ms Boag being asked for their account of the meeting.
Ms Pullar told the Dominion Post the allegations were an attempt to smear her reputation and that of Ms Boag.
"Had I not recorded this meeting, it would have been ACC's word against mine," she told the paper.
Ms Pullar said many ACC clients choose to record their meetings "to protect themselves against these underhand types of tactics".
"No claimant who chooses to go the media after exhausting alternative means to get ACC to take their issues of unlawful conduct and breaches of privacy seriously should have to tolerate this kind of harassment."
Ms Pullar suffered a head injury in a 2002 bicycle accident that she said left her unable to work fulltime, and had been battling with ACC over its assessments of her ability to work.
The Privacy Commission is investigating the leak of the ACC clients' details.
