^Hold on, though. They arrest Reese, and he tells them a story about robotic killing machines and how one of them is chasing Sarah etc etc etc. That story was clearly recorded.
Then, a man meeting the description Reese gave attacks the police station, wipes out most of the officers stationed there but the psychologist who interviewed Reese clearly survives. At no point during what must have been one of the largest criminal investigations in American history (somebody murdered at least a dozen cops after all) did somebody watch that tape ?