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Nicky Hager's book Dirty Politics claims Mr Key's office or the SIS helped Slater obtain the documents, which he then used to embarrass former Labour leader Phil Goff.
In the video, Mr Key referred to the briefing from Dr Tucker while being questioned about the matter during his post Cabinet press conference on August 8, 2011, in the days following the documents' release.
Speaking to media outside Mt Roskill Grammar school this afternoon, Mr Key denied the video was a contradiction.
"No, not at all. In the context of that video, I meant 'my office'. Frankly the demarcation wasn't significant back then.
"Yesterday when I checked, I did a very, very thorough check. I checked with the director at the time. He fully supported the position the ombudsman was independently checked with. She fully supported the position and I know my position is absolutely correct.
"There'll be an inquiry, people will look at all that."
Mr Key said he "probably should have" clarified that it was his office which was briefed over the OIA release, not him. "But, to be honest, that wasn't the big issue at the time."
It was "definitely not the case" that he was briefed about the release while on holiday either, he said. "I'd be more than happy for my phone records to be [seen]."
"There's no dispute that somebody in my office was briefed. I don't think anybody disputed that and, in fact, ultimately the inquiry's undertaken [and] those people will be spoken to.
"The reason I don't name them is because these are people who handle national security issues, and I simply don't want to put their name in the public domain."
Mr Key said he was "100 per cent confident" a member of his office hadn't leaked the information to Slater, and he said he was prepared to go under oath on the issue.
The emergence of the 2011 video came after Mr Key's version of events -- that he was never directly briefed by Dr Tucker on Slater's OIA request -- was backed up yesterday by Dr Tucker and Ombudsman Dame Beverley Wakem.
Inspector General of Intelligence and Security Cheryl Gwyn is investigating the issue after deeming there was "sufficient public interest" to justify her holding her own inquiry to get to the bottom of what happened.
The findings are not expected to be released before the election.
- By Brendan Manning of APNZ and Adam Bennett of the NZ Herald