It's worth noting that outside the US, things are different. Here in Australia, you can't have 'not talking to the police' held against you... unless you were already talking to the police and shut up when they started asking questions. If you were being friendly and shooting the breeze with them, then they starting questions and you shut up, that change in manner can be held against you, for example.

If you're not in the US, it's worth checking out what your own local jurisdiction expects - all the items in the Don't Talk to the Police video still stand (because they're about human psychology, not points of law), so it's worth knowing how much you can just shut up around police.