I disagree entirely. The inverse is actually true. You must talk.
If you don't talk, it WILL hurt you. What you say is more important...and The Supreme Court of the United States agrees with me. Salinas v. Texas
http://www.supremecourt.gov/opinions/12pdf/12-246_7l48.pdf
Petitioner cannot benefit from that principle because it is undisputed that his interview with police was voluntary. As petitioner himself acknowledges, he agreed to accompany the officers to the station and ‘was free to leave at any time during the interview.’ Brief for Petitioner 2 – 3 (internal quotation marks omitted). That places petitioner’s situation outside the scope of Miranda and other cases in which we have held that various forms of governmental coercion prevented defendants from voluntarily invoking the privilege. - Justice Samuel Alito
Justice Alito said that there are only two situations in which the right to remain silent exists without it being explicitly claimed: when a criminal defendant does not take the stand at trial, and when government coercion makes forfeiture of the privilege involuntary. Neither was present here and because Salinas did not expressly invoke the privilege against self-incrimination, the prosecutor could use his silence as evidence against him.
Fundamentally: A person may not invoke the right to remain silent by being silent and not responding to police questions.
From the ABA journal: "For criminal defense lawyers the lesson is clear: they must advise their clients who wish to remain silent to say so explicitly in all contexts. Otherwise, now, their silence before arrest in response to police questions can be used against them." You must explicitly say, "I wish to invoke my right to remain silent."