A report in Harper's magazine said the deaths may have occurred at a previously undisclosed facility a mile or so from the main prison complex.
Prison guards said they knew of the existence of the "black" site and saw three detainees removed from Camp Delta several hours before the deaths were reported.
Those who knew of the facility referred to it as "Camp No" Army Sgt Joe Hickman told the magazine. He said anyone who asked if the black site existed would be told, "No, it doesn't".
At a 7am meeting on June 10, 2006, with 50 or so soldiers and sailors, a commander said the three men had died by swallowing rags, causing them to choke to death.
According to the magazine, they went on to say the media would be told the three prisoners had committed suicide by hanging themselves in their cells, according to Scott Horton, the article's author and a lawyer who has worked on detainee issues.
Admiral Harry Harris, then commander of the base, declared the deaths "suicides" and said the men had killed themselves as a political gesture. "I believe this was not an act of desperation, but an act of asymmetrical warfare waged against us."
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The account, based mainly on interviews with former guards at the US prison on Cuba, suggested the US government was covering up details of what precisely happened in the hours before the deaths.
President Barack Obama has pledged to close the prison, in part because of the damage its reputation for abuses has done to America's image. But difficulties with resettling the majority of the remaining 215 prisoners overseas mean he will miss his own deadline of this Friday.
The three Guantánamo detainees who died the night of June 9, 2006 were Salah Ahmed Al-Salami, 37, of Yemen; Mani Shaman Al-Utaybi, 30, of Saudi Arabia; and Yasser Talal Al-Zahrani, 22, of Saudi Arabia.
In an earlier report into the deaths, the US Naval Criminal Investigative Service found that the men, who were in separate cells, had made nooses out of sheets and T-shirts but somehow fastened them to an eight-foot high mesh wall. They had also somehow bound their own hands, as well as having extra sheets to hang in front of their cell door windows.
Mr Horton claims the report was littered with holes and contradictions, such as the fact that normal Guantánamo conditions do not allow prisoners large amounts of linen.
Other guards have previously spoken or written about their shame at what they witnessed or participated in at the detention centre.