I watched it happen..
Saw it, as it happened, and then, from home, saw the smoke to the right , in the sky, for days. Listened to the sirens for 48 hours passing my home, as they turned Giant's Stadium into a pseudo morgue/staging area. Spoke on a cell phone as a friend was running down the South Tower stairway, assuring me he was alright.
Yes, I'd watch that movie because I find the enormity of that day awe inspiring. The events of that day changed the lives of more people in modern history than any other day. The world changed that day, and if you watch, you can see it happen. Nicholas Cage, as an actor, is a decent guy, with pretty good ethics. He's picked his roles pretty carefully and based on that I'm going to believe (until otherwise shown) that the portrayal of this day is accurate.