"My understanding is, yes, there was a confidentiality agreement with the final settlement," Woods said this morning.
A spokesman for the minister later said she had based those comments on incorrect advice from officials and after seeking more information, had received clarification.
One of Handley's gripes was that he had not heard from anyone over why the role was dropped.
Woods confirmed she hadn't been in touch with Handley yet.
"We made a conscious decision to talk to Mr Handley through officials. I haven't spoken to Mr Handley yet but I haven't ruled out doing so later today."
Curran said today it was Handley's right and his choice to release the information. "I think it's good that it's out there."
Curran said she and the Government were "working through" releasing the information themselves.
"With relation to the Government's process, it is a different process and there are other responsibilities and obligations, and one of the obligations that I had was to respect the process with regard to him."
She denied that it was embarrassing for Ardern.
"No, I think this is part of what happens when there is a controversial issue and transparency is actually occurring. I would like to make the point that the State Services Commission found that the process of the recruitment was very robust and the meeting I had with him in February did not prejudice that process."
An aide-memoire from the State Services Commission to Minister Chris Hipkins earlier this month said the evidence suggested a "suitably robust " recruitment process. It also said that viewed objectively, the meeting did not prejudice the process.