NZDF said the mission was not one of "revenge", as the authors claimed, but to remove a threat to New Zealand's Provincial Reconstruction Team in neighbouring Bamiyan province.
Two weeks before the raid, New Zealand suffered its first casualty in Afghanistan when Lieutenant Tim O'Donnell was killed in a raid believed to have come from combatants in the Tirgiran Valley.
McLeod said their clients had viewed the NZDF material and claimed it contained major inaccuracies.
"'Tirgiran' is not a village, and therefore 'Tirgiran Village' does not exist," the letter stated.
Instead, McLeod's letter said Naik and Khak Khuday Dad villages were inside the area on NZDF's map that identified the target areas for the NZSAS raid.
The villages labelled by NZDF - and also by Hit & Run - as Naik and Khak Khuday Dad - had been labelled incorrectly and were actually villages called Beidak and Khakandy, respectively.
McLeod's letter said: "Tirgiran is the name of the river valley and the greater area depicted on the NZDF map, and the Naik and Khak Khuday Dad villages are within Tirgiran Valley.
"To be completely clear, there is no separate settlement of any kind named "Tirgiran Village", anywhere in the Tirgiran Valley."
The letter was made public by the lawyers shortly before the release of an "analysis" by Hager of the NZDF press conference this week.
In it, he confirms that the book places the villages in the wrong location but said NZDF was wrong on all other major points.
He wrote: "Our conclusion is that the NZDF criticisms are wrong - with one exception - and that they have failed to address almost everything of substance in the book. This is what a cover-up looks like."
Hager said the "location of the raid and the villages is indeed slightly different to what our local sources told us".
But he said it "does not change the story in any significant way".
He said the names of the villages were correct and "all the rest of the story in the book is unchanged".
"Likewise the photos in the book of the villages attacked in the raid are correct, as are the photos of the victims and destroyed houses."
Hager said NZDF had "leaped on" the discrepancy around the location of the raid and "tried to sow doubt about the rest of the book".
"Keating said the 'central premise' of the book was incorrect; that there were 'major inaccuracies - the main one being the location'. But the location is a minor detail, difficult to establish in mountains with no roads or detailed maps.
"Contrary to what Keating said, the central premise of the book is that the actions of the
SAS and its allies in the villages of Naik and Khak Khuday Dad led to civilian deaths and injuries, destruction of houses, neglect of wounded people and then a cover-up - and none of that has changed."
Hager said Keating had not responded to allegations in the book in any detailed way to allow them to be measured against what was in Hit & Run.
But he said there was an important confirmation that the NZSAS were responsible for calling in air support.
Hager said it contradicted an earlier statement in which "ministers suggested that if there had been any civilian deaths they were the responsibility of the United States' pilots, not the New Zealand SAS".
"It confirms what we said in the book: that the SAS commanders in charge of the raid have responsibility for deaths and injuries caused by the US attack helicopters, which they controlled and had requested to be part of the raid."
The letter from the lawyers and Hager's statement repeated calls for an independent inquiry.
Prime Minister Bill English today made his strongest comments defending New Zealand's military against allegations contained in the book, saying it's not up to officials to disprove every claim made by Hager and Stephenson.
English also revealed the camera footage cited by the Chief of Defence as proof SAS raids in Afghanistan were properly conducted belongs to the US military.
"It is one piece of record of the operation. My understanding is that video is something that belongs to the US defence forces," English told Newstalk ZB.
"It may or may not be possible for that to be released. They are responsible to their national command, not to us. That is the sort of issue that the CDF is working through."
Although there was no case for an inquiry into alleged war crimes, English said Keating was required by law to consider other allegations "and make a decision on whether there is basis for an inquiry, and he is still working through that".
"The presence of the allegations does not require the Defence Force to rebut or refute them in every single way. It is up to the people making the allegations to prove, as they stated when they launched the book, that war crimes were committed. They haven't reached that threshold."
