"We can't overlook that and they have fronted up and apologised for it. But someone can't try and blackmail the department to try to get back their child, when there are obviously reasons for that."
Ms Mackenzie said the department had served the woman with an order from the Family Court to prevent publication, and applied to the courts for the return of the document.
"Any institution that holds private information needs to be accountable when there is a breach. However, there is also a responsibility that extends to the person who receives private information in error."
Ms Mackenzie conceded it was the department's mistake in the first place, and it had apologised to the family whose information was involved.
"A mistake has occurred and I'm sorry that our actions have seen a family's private information passed to a third party. It should never have happened, and we've apologised to the family for this."