just for an information, as we don't know where OP is coming from, this is only true in country's who uses the Adversarial system (USA, UK). As with the Inquisitorial system (Western continental Europe), justice (including police) needs to investigate "à charge" and "à décharge", so they are obliged to take the answers that makes you innocent into account. Also, In continental Europe, it's forbidden for the police to lie during an interrogation, in contrast with the USA.

Not answering any questions isn't going to make them seem less guilty. Those laws are meant to protect use from abuse of power from police but claiming not to answer anything from the beginning isn't going to clear his name.

Even in Europe would I say that keeping your mouth shut is a good idea. At least in France.

depends in which Salduz category you are being questioned. If it's in I, you'll be fine. If it's in II, III, IIIbis or IV, use your right to remain silence, as you've been told before the questioning. Unless you have something to bring up in your defence (like an alibi or an "anti-motive"). If it's not in Salduz at all, you'll be fine as well.