You don't know ahead of time what's going to happen. That's the key here. Maybe they'll lie (probably not that common), or maybe what you said will somehow imp

You don't know ahead of time what's going to happen. That's the key here. Maybe they'll lie (probably not that common), or maybe what you said will somehow implicate you in a crime, or maybe...? That's why it's important. It's not after the fact knowing the police lied but beforehand when you don't know how things will play out that remaining silent is important.