The 'right to remain silent' is an American caution. In this country it is "You do not have to say anything. But it may harm your defence if you do not mention when questioned something which you later rely on in court. Anything you do say may be given in evidence."
But if you are in the US it is "You have the right to remain silent. Anything you say can and will be used against you in a court of law. You have the right to be speak to an attorney, and to have an attorney present during any questioning. If you cannot afford a lawyer, one will be provided for you at government expense."
Notice the difference. In a British court, what you say is given in evidence (whether it helps or hinders your case). In an American court, the presumption is that the evidence will be given against you.
Yes grunty, if for example, you say "I'm guilty" this will be used to prove your guilt, whereas if you say "I'm not guilty" this will be used to demonstrate that you are a liar, and thus guilty. Then it's straight of to Cuba for a bit of degradation and torture.