More than one thing can be true about the same event

To Libyans who witnessed the assault and know the attackers, there is little doubt what occurred: a well-known group of local Islamist militants struck without any warning or protest, and they did it in retaliation for the video. That is what the fighters said at the time, speaking emotionally of their anger at the video without mentioning Al Qaeda, Osama bin Laden or the terrorist strikes of 11 years earlier. And it is an explanation that tracks with their history as a local militant group determined to protect Libya from Western influence.

“It was the Ansar al-Shariah people,” said Mohamed Bishari, a 20-year-old neighbor who watched the assault and described the brigade he saw leading the attack. “There was no protest or anything of that sort.”

United States intelligence agencies have reserved final judgment pending a full investigation, leaving open the possibility that anger at the video might have provided an opportunity for militants who already harbored anti-American feelings. But so far the intelligence assessments appear to square largely with local accounts. Whether the attackers are labeled “Al Qaeda cells” or “aligned with Al Qaeda,” as Republicans have suggested, depends on whether that label can be used as a generic term for a broad spectrum of Islamist militants, encompassing groups like Ansar al-Shariah whose goals were primarily local, as well as those who aspire to join a broader jihad against the West.

But in the heated election-year American political debate such distinctions have been lost, scholars said, as the administration has framed the attack around the need for American outreach to the Arab world, while Republicans have focused on the perils of American weakness there.

And the result has produced accounts at great variance with what witnesses said they saw.

To those on the ground, circumstances of the attack are hardly a mystery. Most of the attackers made no effort to hide their faces or identities, and during the assault some acknowledged to a Libyan journalist working for The New York Times that they belonged to the group. And their attack drew a crowd, some of whom cheered them on, some of whom just gawked, and some of whom later looted the compound.

The fighters said at the time that they were moved to act because of the video, which had first gained attention across the region after a protest in Egypt that day. The assailants approvingly recalled a 2006 assault by local Islamists that had destroyed an Italian diplomatic mission in Benghazi over a perceived insult to the prophet. In June the group staged a similar attack against the Tunisian Consulate over a different film, according to the Congressional testimony of the American security chief at the time, Eric A. Nordstrom.

At last week’s Congressional hearing, Mr. Nordstrom tried to contradict lawmakers who insisted the group was at least “loosely affiliated with Al Qaeda.”

Representative Dan Burton, Republican of Indiana, cut him off. “Don’t split words,” he said. “It is a terrorist organization.”