I don't know. It has support from all of the families of the deceased and comes a full 5 years after the event. Movies about Vietnam and WWII came out during those wars. They are 3 very different events, but still touched the people of the times whether hippies, Jewish, etc.

Some quotes about the movie from family members of the passengers:

--"When Paul and Lloyd came to us, they were very concerned about being as accurate as they could possibly be," Ms. O'Hare said, and they promised to represent all the passengers, not just a few. "It's nice that you can include them all, and honor them all," she said.--

--"I don't know what the good time is" to make these movies, said Carole O'Hare, the daughter of Hilda Marcin, one of the 40 passengers and crew on Flight 93. "I do know that prior to this date, it would not have been a good time. We all knew it would come eventually," she said, and "given the opportunity for input and involvement, I would rather have my say than be put in the background. Even if it doesn't come out as you envisioned it," she added, "at least you know you did your best to have your say."--

What inspired the director about doing the film:

--For Mr. Greengrass, though, it was the story's broader implications that inspired him to make "Flight 93." "Forty ordinary people had 30 minutes to confront the reality of the way that we're living now, decide on the best course of action and act," he said. The passengers were the "first people to inhabit the post 9/11 world," he continued. "They had to choose because they were in that airplane. Their choices are our choices, and their debate is our debate."--

So, my opinion is that it's ok with respect to how long since the event and the most important factor (for me personally) is the making of the film in regard to and accuracy and respect.
I do know that if the film came out this week, no matter how well it was made, I would choose not to see it.

How exactly can this film be accurate? How many facts can they gather from a few short cell phone calls from panic stricken passengers?

Yeah. Again, from the article linked to their homepage, they say no one will ever know (and therefore reproduce) exactly what transpired. The actors just talked to the families, watched old videos of the victims, tried to learn about them and then improvised much of the responses during the filming based on what they learned.

Wonder who the terrorist-actor talked to? ;)