In the documentary, Fahrenheit 911, it is said that Osama Bin Laden's family members were flown out of the United States just days after the 9/11 terrorist attacks, and during a time when there was a ban on all air travel.
Is this true?
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They were flown out, but not when air travel was banned.
Firstly, civilian air traffic was allowed to resume "at 11 a.m. EDT [eastern daylight time] Thursday [13 September 2001]", so there was only about a 48 hour period where flights were prohibited.
As explained in a 30 September 2001 New York Times article:
Both planes, one jumbo jet carrying 100 family members, and the other 40, were eventually allowed to leave when airports reopened and passports were checked
The young members of the bin Laden clan were driven or flown under F.B.I. supervision to a secret assembly point in Texas and then to Washington from where they left the country on a private charter plane when airports reopened three days after the attacks.
Adding to DavePhD's answer, a little digging shows that Richard Clarke, the Chief of Counterterrorism at the time, took sole responsibility for approving the flights:
Moore, on his website and in The Official Fahrenheit 9/11 Reader, points to additional statements by Richard Clarke, also published in The Hill, which he believes support his contention that the White House approved the flights. The following is a chronological summary:
September 3, 2003:
In his testimony before the Senate Judiciary Committee's Subcommittee on Terrorism, Clarke said: "It is true that members of the bin Laden family were among those who left. We knew that at the time. I can't say much more in open session, but it was a conscious decision with complete review at the highest levels of the State Department and the FBI and the White House."
March 24, 2004:
In testimony to the 9/11 Commission, Clarke indicated that the request was not abnormal, "The Saudi embassy, therefore, asked for these people to be evacuated; the same sort of thing that we do all the time in similar crises, evacuating Americans. The request came to me and I refused to approve it." He goes on to explain that the FBI eventually approved the flights and he describes conversations in which the FBI has said that there was no one who left on those flights who the FBI now wants to interview.
March 24, 2004:
"I would love to be able to tell you who did it, who brought this proposal to me, but I don't know. The two – since you press me, the two possibilities that are most likely are either the Department of State or the White House Chief of Staff's Office. But I don't know."
May 25, 2004:
In an interview with The Hill newspaper, published the following day, Clarke said: "I take responsibility for it. I don't think it was a mistake, and I'd do it again." He went on to say that "It didn't get any higher than me... On 9–11, 9–12 and 9–13, many things didn't get any higher than me. I decided it in consultation with the FBI."
Here's the source: