The NSA was pulling a Batman Gambit.Why would the NSA arrest Telly when if they just let the local cops handle it, everyone would continue to believe she was delusional? They wouldn't... if they didn't want the conspiracy to unravel. Remember the NSA was under the thumb of the aliens and there was nothing they could do about it. They couldn't even tell anyone since they would just be sucked away. They arrested Telly because they wanted to raise people's suspicions. It was the only way to make the heroes aware something was up while seeming compliant to the aliens.
Telly is genuinely schizophrenic, and the whole incident was one of her delusions.This explains why no information on the plane crash and the lost children exists anymore; there was none to begin with. Things such as the disappearing photos, the people snatched into the sky, the mysterious doctor, came from the film being centered in Terry's own mind; we would be watching the scene unfolding through her eyes. Her defiance of the doctor, and "rediscovery" of her son on the playground are her return to reality.
The original writers got bored mid-way through the film and some monkeys were hired to finish it.This would explain why the beginning is a cool setup for a movie about a woman with a mental illness and ends up being a movie about a woman who is perfectly healthy, but aliens are messing with her mind.