COMMENT: The Operation Burnham inquiry is finding something remarkable in New Zealand's elite soldiers: red faces, vague memories, evasive answers, and a thin story.

Consider what you're being asked to believe. A Special Air Service (SAS) led raid of Afghanistan villages in 2010 has nine insurgents killed, then possible civilian deaths are confirmed. 

But an SAS commander mistakes an acronym while glancing at a paragraph of a report, and emails headquarters to say everyone is cleared of the possible deaths. 

The Chief of Defence Force is among high-ranking officers who overlook obvious evidence, and assures the Defence Minister all is well. 

Until a highly-classified report, which exposes what is either a mistake or falsehood, mysteriously emerges from a locked safe in Wellington three years later. 

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Former defence chief Sir Jerry Mateparae​ has, along with a handful of senior officers, already confessed they gave the defence minister bad advice in 2011 - which led New Zealand to think allegations of civilian deaths were "unfounded" for three years.

But the explanation given by the SAS has hardly convinced the inquiry's lawyers, who have accused some commanders of lying.

And in moments the masters of this convenient narrative appear almost exposed.

Brigadier Chris Parsons, the highly-educated SAS commander who apparently mistook an acronym commonly used by the New Zealand forces, was forced to make a red-faced admission under questioning on Tuesday. 

"Don't look at them," said inquiry lawyer Kristy McDonald, QC, as Parsons turned to the Defence Force lawyers.

He admitted to being primed to recall a detail his written evidence didn't cover, over the lunch break. 

The question of witness tampering hung in the air, and continues to return when witnesses delete aspects of their evidential statement - prepared with legal assistance - that doesn't quite fit their knowledge of events.

Most of these witnesses admit a degree of fault, with a patchy memory replaced by confidence they would have taken the right action — "If I knew about the report".

This International Security Assistance Force (ISAF) report, deemed by witnesses to be "conclusive" despite other evidence that included gun tapes, was clearly hidden from view. Yet no-one will admit this.

Commodore Ross Smith, chief of staff in 2014, said his "stomach dropped" when the report was discovered but couldn't adequately explain how it got there, or how he later forgot about it. 

Colonel Michael Thompson received the bundle containing the report and placed it in the safe in 2011. From who? He can't recall.

Lieutenant General Rhys Jones, an Army-man turned chief of defence in 2011, said he was told the Defence Force didn't have the report when he took up the role.

He says Jim Blackwell, an SAS commander possibly in charge during a time the document may have fallen into Defence Force hands, likely told him this.

"Where is he now?," asked Davey Salmon, lawyer for the authors of Hit & Run.

Lieutenant General Tim Keating began his evidence on Wednesday. An SAS soldier turned top brass, he was chief of staff under Mateparae when the allegations first went to ground. 

"There were missed opportunities for us to clarify that fact that civilian casualties may have occurred," he said.

"One of the first lessons that we learn in the military is integrity ... and the basis of the integrity is when you make a mistake, you fess up."

Yet he could recall no mistakes he made.