I abhor Chicken Little-ism too, but as the woman says in the video as she's watching:
"This isn't normal. An airliner (she couldn't ID it as presidential transport) with a fighter... it must be a hijacking!"
That's pretty sound reasoning, especially if the last time you saw an airliner that low it was plowing into a building.
As for offices evacuating, etc... if you were at your desk in a hi-rise and saw that, especially if the last time you saw that it was plowing into a building, would
you wait until someone checked with the FAA, or would you hit the stairs? If I were at the next desk, you wouldn't be able to ask me wat i think, because I'd be gone.
The jittery citizens of NYC
do need educating about these things, but surprises are not the way to do it.
Confirmation that the local rags and TV had picked up the word of this scheduled event early on, and that people in general were aware, would be a good start.