Stanzel was responding to questions about a New Yorker magazine report quoting retired Major-General Antonio Taguba, as saying "the president had to be aware" of the abuse of prisoners by US military guards.
Taguba also said Donald Rumsfeld, the former defence secretary who had initially denied knowledge of the lurid photographs of prisoner abuse, was at best, "in denial".
"The photographs were available to him – if he wanted to see them."
Referring to Rumsfeld's May 7, 2004, testimony before congress in which he said he had no idea of the extent of the abuse, Taguba said Rumsfeld was "trying acquit himself, and a lot of people are lying to protect themselves".
He said Rumsfeld and the military's top brass who stood with him as he misrepresented what he knew about Abu Ghraib had failed the nation.
The photographs taken by US jailers humiliating prisoners who were naked or hooded, on leashes or piled in a pyramid, became one of the few things Bush said he regretted about the Iraq war and apologised for on May 6, 2004.
Taguba spoke of other, undisclosed material, including descriptions of the sexual humiliation of a father with his son, who were both detainees and "a video of a male American soldier in uniform sodomising a female detainee" that was never made public or mentioned in any court.
Taguba said that all high-level officials had avoided scrutiny while the jail keepers at Abu Ghraib were tried in courts-martial.
Warnings and consequences
"From what I knew, troops just don't take it upon themselves to initiate what they did without any form of knowledge of the higher-ups," Taguba told the New Yorker, adding that his orders were to investigate the military police only, and not their superiors."
Eleven US soldiers have been convicted for abuses related to detainees at Abu Ghraib.
"These [military police] troops were not that creative," he said.
"Somebody was giving them guidance, but I was legally prevented from further investigation into higher authority."
Seymour Hersh, who interviewed Taguba for the New Yorker, told Al Jazeera that Taguba had been warned by General John Abizaid, the then commander of the US Central Command, that he would be investigated along with his report.
"I'd been in the army 32 years by then, and it was the first time that I thought I was in the Mafia," Taguba said.
Taguba was told to retire by January 2007 and was offered no reason.
He said he was "ostracised for doing what I was asked to do".
Well aware that his former military colleagues would be angry at his speaking out, the retired general said: "The fact is … we violated the tenets of the Geneva Convention. We violated our own principles and we violated the core of our military values.
"The stress of combat is not an excuse, and I believe, even today, that those civilian and military leaders responsible should be held accountable.