At that meeting ACC claims Ms Pullar attempted to strike a deal to exchange the private information of thousands of other ACC claimants in return for a guaranteed benefit.
It subsequently emerged that Dr Smith, who was ACC Minister, wrote two letters supporting his old friend Ms Pullar's pursuit of her ACC claim, errors for which he resigned last week.
Ms Collins said the investigation, which she was told of early yesterday after a discussion with Ms Shroff on Tuesday night, was a "very good idea".
The commission's work "may involve computer forensic investigation", she said. "Frankly I welcome that."
Labour has been pressing for the Auditor-General to investigate Ms Pullar's use of her political connections to advance her ACC case and the role of ACC's board in setting up the December meeting.
In Parliament yesterday, Labour's Trevor Mallard questioned Ms Collins on her handling of Ms Boag's email, asking whether she or any of her staff discussed its contents with Mr Lusk.
Ms Collins said she had not, but Labour's deputy leader, Grant Robertson, pressed the attack later in a general debate.
"We know there are many National Party figures involved in this, with the mention of Simon Lusk's name. So we want to know about Simon Lusk's phone calls to Judith Collins' office."
Mr Robertson called on Ms Collins to ensure all emails in and out of her office, text messages and phone calls were made available to the Privacy Commissioner.
Mr Lusk was the manager of the Vote for Change campaign against MMP last year and among other roles has served as Napier MP Chris Tremain's campaign manager, in 2008.
WHO SAW EMAIL
* Michelle Boag (above) - the sender of the email and Bronwyn Pullar's friend and supporter.
* ACC Minister Judith Collins - the recipient of the email who then forwarded it to:
* ACC chief executive Ralph Stewart and his secretary, and:
* ACC chairman John Judge.