[demallien]

This is true, but inferences from silence are much more problematic when you haven't said anything. If I tell the police a story about what I had been up to that afternoon, and then they say "right so if that's true, why was the victim's blood on your shoes?", and I choose at that point not to answer, it's suspicious, and can be played as such in court.

If, on the other hand, I have said nothing other than "I'm not speaking without discussing with my lawyer first", it's much easier for your legal counsel to paint you as just a cautious individual, rather than someone that is trying to cover up a lie.

tldr, "don't talk to the police" is also good advice in Commonwealth countries, not just the US.