The Fifth Amendment guarantees that no person may be compelled to be a witness against himself in a criminal case. It follows that a violation occurs when a suspect is compelled to answer questions and those answers are introduced in a criminal trial. The government can and does compel people to speak (or otherwise communicate) all the time. All of us who recently filed our tax returns are keenly aware of that. If the statements are not incriminating, there is no Fifth Amendment violation. Even if they are incriminating, if the person is guaranteed they won't be used against him in a criminal trial, such as by a grant of use immunity, there is no Fifth Amendment violation. No, you don't "have a right to remain silent" as such. The right is narrower than that.
What the Supreme Court did in Miranda v. Arizona was create a rule of evidence for criminal trials. If the police question a suspect and don't follow the rules laid down in that case, the suspect's statements are conclusively presumed compelled and therefore cannot be admitted at the suspect's trial. That's it. The court did not make a law requiring police to Mirandize everyone they arrest. There is no right to the warnings as such. There is no right to have counsel present during questioning as such. An arrestee cannot sue the cops for questioning without Miranda warnings. Although the Supreme Court case of Chavez v. Martinez, 538 U.S. 760 (2003) is a jumble of opinions, that much at least is clear.
Beating a confession out of an arrestee that is never used in a trial is, of course, a violation of his rights. It is a due process violation, and the arrestee can sue for that. See the very brief Part II of Justice Souter's opinion in Chavez, which is the opinion of the Court on that point. The Miranda requirements are prerequisites for introducing the fruit of the interrogation at trial, period. Questioning for other purposes is not subject to these requirements. They still can't beat him, of course, but that has nothing to do with Miranda. It's not even the Self-Incrimination Clause* at issue in that circumstance.
With the nature of the rule clearly in mind, let us turn to the exception.
The question before the Supreme Court was not whether the police officer had violated a right of Quarles at the moment he asked the question but rather whether the answer was admissible at trial.
We hold that, on these facts, there is a "public safety" exception to the requirement that Miranda warnings be given before a suspect's answers may be admitted into evidence...Does the public safety exception of Quarles extend beyond the kind of very brief and urgent questioning involved in that case to a more extended questioning to gather intelligence? It does not matter as long as we don't need the answers for evidence in the bomber's trial.
Joel Achenbach and Robert Barnes report in the WaPo:
Authorities have not read him his Miranda rights, which include the right to remain silent and the right to an attorney. Federal law enforcement officials said they plan to use a public safety exception, outlined in a 1984 Supreme Court decision, "in order to question the suspect extensively about other potential explosive devices or accomplices and to gain critical intelligence."
A delay in issuing Miranda warnings is justified when suspected terrorists are captured in the United States, according to a 2010 memorandum from the Justice Department. But on Saturday, the American Civil Liberties Union warned against too broad of an interpretation of that public safety exception.
"Every criminal defendant is entitled to be read Miranda rights. The public safety exception should be read narrowly. It applies only when there is a continued threat to public safety and is not an open-ended exception to the Miranda rule," said Anthony D. Romero, the ACLU executive director.
The Miranda warning would come into play only if prosecutors planned to use any incriminating statements Tsarnaev might make against him. Federal authorities may feel they already have amassed much evidence against the teenager.
The last sentence is correct, and Romero's statement is nonsense. Nobody is entitled to be read Miranda rights. It is only a prerequisite for evidence admissibility.
* In the initial version of this post I wrote "Fifth Amendment" at this point. I was thinking of local police, for whom the relevant Due Process Clause is in the Fourteenth Amendment. For federal agents, though, the relevant Due Process Clause is in the Fifth Amendment.