We know this because of things Reuters, the New York Times and the Washington Post reported in March 2011 and because of something then-Secretary of State Hillary Clinton said in her final testimony before the Senate Foreign Relations Committee in January.
Obama announced he had ordered the U.S. military to intervene in Libya's revolution on March 19, 2011, stressing that U.S. military involvement would come exclusively via air.
"We will not -- I repeat -- we will not deploy any U.S. troops on the ground," he said.
Ten days later, in an interview with NBC News, Obama suggested he might provide arms to the Libyan rebels. "I'm not ruling it out, but I'm also not ruling it in," he said.
That same day he told ABC News: "I think that it's fair to say that if we wanted to get weapons into Libya, we probably could."
Two days later, the New York Times, following up on a Reuters story, reported that Obama had already signed a finding authorizing covert aid to the Libyan rebels -- and noted that the administration had not actually started delivering arms to these rebels.
"Several weeks ago, President Obama signed a secret finding authorizing the CIA to provide arms and other support to Libyan rebels, American officials said Wednesday" the Times reported. "But weapons have not yet been shipped into Libya, as Obama administration officials debate the effects of giving them to the rebel groups."
The Washington Post chimed in with its own report: "President Obama has issued a secret finding that would authorize the CIA to carry out a clandestine effort to provide arms and other support to Libyan opposition groups."
The day before Obama indicated he was not ruling out arming the Libyan rebels, Adm. James Stavridis, commander of U.S. European Command, hinted at why this might not be a good idea.
"We have seen flickers in the intelligence of potential al-Qaida, Hezbollah," Adm. Stavridis told the Senate Armed Services Committee of the Libyan rebels. "We've seen different things. But at this point, I don't have details sufficient to say that there's a significant al-Qaida presence or any other terrorist presence in and among these folks. We'll continue to look at that very closely."
A Reuters reporter asked Secretary Clinton that day about Adm. Stavridis's testimony: "Is that part of the U.S. debate over any potential arms transfers to the transitional council?
"We do not have any specific information about specific individuals from any organization who are part of this, but of course, we're still getting to know those who are leading the Transitional National Council," Clinton said. "And that will be a process that continues."
In plain English: the Obama administration jumped into backing the Libyan rebels before it knew how extensively those rebels were tied to al-Qaida.
Bruce Riedel of the Brookings Institution, a former CIA analyst and Obama adviser, elaborated on Adm. Stavridis's testimony for National Public Radio.
"I think the admiral was going with a good hunch, which is they [al-Qaida] are a small minority [among Libyan rebels], but we need more than a good hunch now," said Riedel.
"We have Libyans in the senior hierarchy of al-Qaida today," Riedel said. "We have Libyans fighting with al-Qaida in Afghanistan, against NATO forces, today. So there is a longstanding pattern of Libyans being associated with al-Qaida and likeminded groups."
In her final Senate testimony as secretary of state, Clinton conceded that arms had gone from post-revolutionary Libya to al-Qaida -- while suggesting the weapons "liberated" by the revolution mostly came from Moammar Gadhafi's stocks.
"Libya was awash in weapons before the revolution," said Clinton. "Obviously, there were additional weapons introduced, but the vast, vast majority came out of Gadhafi's warehouses and were ... liberated and then went on the black market, were seized by militias, seized by other groups and have made their way out of Libya into other countries in the region and have made their way to Syria, we believe."
"There's no doubt that the Algerian terrorists had weapons from Libya," Clinton said. "There's no doubt that the Malian remnants of AQIM [al-Qaida in the Islamic Maghreb] have weapons from Libya."
The CIA declined to comment on the question of whether the reports in the New York Times and elsewhere about the covert finding Obama allegedly signed regarding the Libyan rebels were accurate. A CIA spokesman did say, however, that the agency takes seriously its duty to inform Congress about covert activities.
"Without speaking to or confirming any alleged finding," a CIA spokesman said. "I can say that the CIA takes its responsibility to keep Congress fully and currently informed on intelligence matters -- to include covert action -- seriously."
Did arms go from the United States to Libyan rebels to al-Qaida? Or did U.S.-backed Libyan rebels give Gadhafi's arms to al-Qaida? Where did the terrorists who attacked the U.S. compound in Benghazi get their weapons?
These are important questions that will only be answered if the House of Representatives approves the resolution Rep. Frank Wolf has put forward and convenes a special committee to investigate what truly happened in Libya.
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