I don’t think you understood my point. You seem to have missed an important difference in meaning between “verified” and “verifiable”.
“Three angels can dance on the head of a pin” is not a verifiable statement. It can’t be proven true or false. “There are three cats in this bag” is readily verifiable, even if that fact has not yet been verified.
Their claims were readily verifiable at the moment they made them; they were verified when the video was released.
Knowing that the police would want to paint themselves in as positive light as possible, and knowing how bad they would look in getting caught making so blatant a lie, trusting their statement was not unreasonable.