Boyle gave the statement shortly after landing in Canada late yesterday with his American wife, Caitlan Coleman, and three young children.
The couple was rescued on Wednesday, five years after they had been abducted by the Taliban-linked extremist network while in Afghanistan as part of a backpacking trip.
Coleman was pregnant at the time and had four children in captivity.
The birth of the fourth child had not been publicly known before Boyle appeared before journalists at the Toronto airport.
Boyle said his wife was raped by a guard who was assisted by his superiors. He asked for the Afghan government to bring them to justice.
"God willing, this litany of stupidity will be the epitaph of the Haqqani network," he said.
He said he was in Afghanistan to help villagers "who live deep inside Taliban-controlled Afghanistan where no NGO, no aid worker and no government has ever successfully been able to bring the necessary help."
Coleman, who is from Stewartstown, Pennsylvania, sat in the aisle of the business-class cabin wearing a tan-colored headscarf.
She nodded wordlessly when she confirmed her identity to a reporter on board the flight. In the two seats next to her were her two elder children. In the seat beyond that was Boyle, with their youngest child in his lap.
US State Department officials were on the plane with them.
The handwritten statement that Boyle gave the AP expressed disagreement with US foreign policy.
He nodded to one of the State Department officials and said, "Their interests are not my interests."
He added that one of his children is in poor health and had to be force-fed by their Pakistani rescuers.
The family was able to leave the plane with their escorts before the rest of the passengers. There was a short delay before everyone else was allowed out.
Dan Boyle, Joshua's younger brother, said outside the family home in Smith Falls, Ontario, that he had spoken to his brother a few times in the past few days.
"He's doing very well. He sounds a lot like how he sounded five years ago. He sounds like he had his head on his shoulders and his wits about him," he said.
"Today, we join the Boyle family in rejoicing over the long-awaited return to Canada of their loved ones," the Canadian government said.
Pakistan's Foreign Ministry spokesman, Nafees Zakaria, said the Pakistani raid that led to the family's rescue was based on a tip from US intelligence and shows that Pakistan will act against a "common enemy" when Washington shares information.
US officials have long accused Pakistan of ignoring groups like the Haqqani network.
US officials consider it a terrorist organisation and have targeted its leaders with drone strikes. But the Haqqani group also operates like a criminal network. Unlike the Islamic State group, it does not typically execute Western hostages, preferring to ransom them for cash.
President Donald Trump, who previously had warned Pakistan to stop harboring militants, praised Pakistan for its "cooperation on many fronts." On Twitter, he wrote yesterday that the US is starting to develop "a much better relationship with Pakistan and its leaders."
The operation appeared to have unfolded quickly and ended with what some described as a dangerous raid, a shootout and a captor's final, terrifying threat to "kill the hostage."
US officials did not confirm those details.
A US military official said that a military hostage team had flown to Pakistan Wednesday prepared to fly the family out.
The team did a preliminary health assessment and had a transport plane ready to go, but sometime after daybreak Thursday, as the family members were walking to the plane, Boyle said he did not want to board, the official said.
Another US official said Boyle was nervous about being in "custody" given his family ties.
He was once married to Zaynab Khadr, the older sister of former Guantanamo Bay detainee Omar Khadr and the daughter of a senior al-Qaida financier. Her father, the late Ahmed Said Khadr, and the family stayed with Osama bin Laden briefly when Omar Khadr was a boy.
The Canadian-born Omar Khadr was 15 when he was captured by US troops following a firefight and was taken to the US detention center at Guantanamo Bay. Officials had discounted any link between that background and Boyle's capture, with one official describing it in 2014 as a "horrible coincidence."
The Haqqani network had previously demanded the release of Anas Haqqani, a son of the founder of the group, in exchange for turning over the American-Canadian family. In one of the videos released by their captors, Boyle implored the Afghan government not to execute Taliban prisoners, or he and his wife would be killed.
US officials have said that several other Americans are being held by militant groups in Afghanistan or Pakistan.
They include Kevin King, 60, a teacher at the American University of Afghanistan in Kabul who was abducted in August 2016, and Paul Overby, an author in his 70s who had traveled to the region several times but disappeared in eastern Afghanistan in mid-2014.
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