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Peters' claim for a breach of privacy was last year rejected by Justice Geoffrey Venning in the High Court, and he was ordered to pay nearly $320,000 in costs.
But he has brought the case back to court in Wellington's Court of Appeal this morning, arguing against the judge's decision.
After a two-week hearing in Auckland in 2019, Justice Venning ruled Peters' privacy was deliberately breached in the lead-up to the 2017 general election to publicly embarrass him and cause him harm.
But his claim for damages and declarations against former government ministers Paula Bennett and Anne Tolley, State Services Commissioner Peter Hughes, the Ministry of Social Development (MSD) and its former chief executive Brendan Boyle was dismissed.
In his decision, Justice Venning said Peters was "not able to establish that they were responsible for the disclosure of the payment irregularity to the media".
In court today, Peters' lawyer Brian Henry began by pointing out the superannuation application should never have been processed in the first place, because it was incorrectly filled out.
"This is a mistake. This is an application form that was not complete, that His Honour correctly accepted should not have been processed as it stood."
Henry said it was a breach of Peters' privacy that Hughes and Boyle chose to brief Bennett and Tolley on the matter, when an investigation had already revealed the mistake was not a result of an intention to mislead or defraud.
He rejected the argument the briefings were to assure the ministers of the integrity of the system.
"We have one very simple proposition. Short of fraud, no private details of any social welfare beneficiary should be disclosed," he said.
"[MSD] receives rafts of information, particularly rafts of information around the sexual behaviour of applicants . . . it is the most personal, private information, and to get the benefit of course you have to fill that out.
"They simply went and disclosed personal facts of Mr Peters, potentially embarrassing facts of Mr Peters . . . all they're doing is providing to a minister salacious information that the minister can do nothing with."
Another reason the information was disclosed was because another member of Parliament, Metiria Turei, had received a large amount of publicity about historic welfare payments.
Justice Venning found that, while Peters had a reasonable expectation his details would be kept private, the disclosure by the public servants to their ministers were, "in the particular circumstances of this case, for a proper purpose and the ministers had a genuine interest in knowing the details of the payment irregularity".
But Henry also argued against that point today, saying "the fact another politician has committed fraud and brazenly tells the media that is utterly irrelevant to Mr Peters' privacy".
He said every member of the New Zealand public had an expectation that politicians would not be getting their private information out of social welfare.
"The private details of any social welfare beneficiary, except in the case of fraud, is too personal for ministers to know."
The integrity of the system could be ensured by the use of the State Services Commission, which was used in this case, he said.
Henry referred to MSD having a tiger in their midst, knowing if it were to be released it would cause damage.
"The more people know, the greater the risk of this tiger escaping.
"Any dissemination of Mr Peters' private information beyond what it was absolutely needed for inside the department is on any test of repugnancy, repugnant."
The matter was a "political very hot potato".
The hearing continues.