Ms Pullar also said the recording shows ACC's account of what was said at the meeting regarding details of the privacy breach and how it occurred was also incorrect.
However Ms Pullar refused to release the recording or a transcript, saying it contained sensitive personal health information.
In an extract of the transcript published yesterday, Ms Boag is quoted as saying: "I don't want to see headlines criticising the minister and the Government for things that have taken place ... And as I say, I mean we are all supportive of this Government. We do not want to see them embarrassed."
Yesterday, Ms Pullar said ACC had published the account of the meeting in which the extortion allegations were made without asking her and Ms Boag if there was any truth to them.
She had given ACC chief executive Ralph Stewart and others at the corporation the opportunity to listen to the recording.
"Despite ACC having heard a full recording of the meeting they have refused to correct their blatant lie, which continues to smear my reputation and Michelle Boag's."
But Labour's ACC spokesman Andrew Little said irrespective of what happened in the meeting, ACC had still asked for the information to be returned and Ms Pullar had not met that request until the story went public in March.
Mr Little said Ms Boag's subsequent email to ACC Minister Judith Collins after the story of the privacy breach broke clearly suggested some kind of deal had been discussed.
"Even if it wasn't about two years of entitlements, clearly some sort of arrangement was being talked about that was some sort of quid pro quo.
"Today's story, if it does anything, just confirms that the ACC officials may have misled the minister in their report, but it doesn't remove any of the cloud of doubt about the actual nature of the conversation that some deal was being struck to return information that she shouldn't have ever had in the first place."
Mr Little said the report highlighted the need for the various official inquiries into the matter "to hurry up and get on with the job, get some conclusions from some credible sources that we can start to see where the truth might actually lie".
However, Green Party ACC spokesman Kevin Hague said the public would have got the impression from ACC that Ms Pullar went into the December meeting demanding two years' compensation and threatening all sorts of consequences, "and very clearly that didn't occur in that meeting".
Mr Hague said the fact that ACC didn't refer the matter to the police immediately "gives rise to the suspicion that the complaint was essentially designed as a diversion from the scrutiny on its own actions".
"That suspicion is given added weight by the revelations today."
Neither Ms Collins nor ACC would comment on the report yesterday, saying it was not appropriate to do so given the matter was under investigation by various authorities.