But Ms Pullar - who attended the meeting with Ms Boag as her support person - secretly taped the encounter.
Last night, TV3's 60 Minutes interviewed Ms Pullar and played part of the recording showing she made no such threat. The link between the accidentally released information and its possible use by Ms Pullar in the media was made by one of two ACC staff members in the meeting.
"The fact is the meeting was totally about getting Bronwyn back to work,'' Ms Boag told TV3. "It was nothing to do with [getting more money from] ACC.''
Green Party ACC spokesman Kevin Hague told the media last night Ms Collins needed to act decisively to restore public trust in the corporation.
"The further revelations about shonky assessment and claims handling practices ... mean that, at the very least, the ACC Minister should remove John Judge as ACC chair.''
On 60 Minutes, Ms Pullar also attacked the corporation for what she described as biased systems.
The former businesswoman said that in 2009, ACC referred her to an independent medical specialist for her ongoing head injury.
Ms Pullar said she had been assured by both ACC and the specialist that he acted separately from the corporation. But an investigation later found ACC medical adviser Anthony Burgess had been in contact with him.
Transcripts of emails from Dr Burgess, whom Ms Pullar has never met, showed that he had passed his own conclusions on to the specialist.
And in a separate email to an ACC staffer, Dr Burgess wrote: "What is incredulous is how this woman has fleeced ACC for seven years.
"From my inspection of this case, it looks very much like the client has manipulated a clinician into providing an inaccurate report for the sole purpose of providing financial gain, or in more direct terms, fraud.
"She can take her narcissistic personality disorder and get back to work.''
ACC was forced to apologise to Ms Pullar for Dr Burgess' behaviour when it was revealed he had been in contact with the independent specialist.