Siddiqui, 36, was arrested in the central town of Ghazni on July 17 by Afghan police who said they believed she had been planning a suicide attack.
She has been described by US officials as a "treasure trove" of information on Al-Qaeda.
Her arrest was the first time in five years she had been seen publicly and her family and lawyers allege she had been held captive since disappearing in Pakistan in 2003 – possibly in a secret US or allied prison.
The US military based at Bagram, about 60 kilometres (35 miles) north of Kabul, said Siddiqui had only been to the base for military treatment for gunshot wounds after her arrest, and not before that.
"She has never been held in US military custody," spokeswoman Lieutenant Colonel Rumi Nielson-Green told AFP.
But outside observers have begun to doubt the credibility of the US military's claims. Sam Zarifi, Asia-Pacific director for Amnesty International, called the government's account "extraordinary" in an interview with National Public Radio (NPR).
"It seems extraordinary to imagine that four U.S. agents who'd gone to pick her up — two military, two FBI — along with at least two Afghan translators, were somehow surprised by this woman, who overpowered them, grabbed a gun, flipped the safety, fired off a couple of shots, and then could only be subdued by shots to the torso," said [Zarifi].
"If the story suggested by the U.S. government is accurate, it paints a very unflattering picture of the competence of forces who are literally on the frontlines of the 'war on terror,'" he said. "If the U.S. story is not true, then we're looking at a serious breach of U.S. and international law when a prisoner in custody is shot."