"She made threats that if her demands were not met she would not return the information and she would inform the media of the alleged privacy issue,'' the report said.
It also said Ms Pullar gave no specific details about the information she had been sent.
Ms Pullar has denied the allegations, saying she made no demands of ACC or threats against it. Former National Party president Michelle Boag, who supported Ms Pullar at the December meeting, has also rejected ACC's allegations.
The Dominion Post reported today that a recording of the meeting, provided to the newspaper by Ms Pullar, was "at odds with'' ACC's story.
It reportedly reveals that neither Ms Pullar nor Ms Boag threatened to go to the media or withhold the information, and that ACC was given specific details about the breach.
Speaking to TVNZ's Breakfast today, Mr Key raised questions about the recording.
"Yes there appears to be a difference of opinion although, as we know with recordings, that it might not be the entire recording,'' he said.
"I'm not saying it is or it isn't, I simply don't know, but the important point there is that there are three investigations going on ... and I'm sure they'll look at all of the information that's there.''
Along with police, the Privacy Commissioner and the Auditor General have launched inquiries into the incident.