I think a major qualifier for that video is "if you're suspect of a crime". In the post, our main character claims to not have expected to come under suspicion.
Do you disagree? Are there examples where you would talk to the police? For example, if your home was broken into?
The point is that anything you say can be used against you for any of an infinity of possible crimes, while it can never ever help you at all.
Though clearly the situation here is not one where the victim was invited to speak, if he had taken the advice to heart, he would have realized that speaking to the police in any capacity is extremely dangerous, and perhaps averted this disaster.