Seibert's handicapped 12 year old son died. Because he had bedsores, she was afraid that she would be charged with child neglect. To avoid criminal charges, she and her two other sons (and some of their friends) conspired to dispose of the body by burning their trailer down. In order to avoid the appearance that the now-deceased handicapped kid had been unattended at the time of the fire, they decided to burn a mentally ill kid (this one alive) with him.
Seems legit, right?
So they did, and the mentally ill kid (who had been living with these fine people) burned to death. And the police figured it out. In order to secure a confession, the police employed a question-first interrogation tactic. Seibert was awakened in the early morning at the hospital where one of her living kids was being treated for burns, arrested, taken to the station, and interrogated at great length until she eventually confessed. This sounds like it was a pretty intense interrogation, too... the detective kept squeezing her arm and repeating "He was meant to die in his sleep." After half an hour of that, Seibert did confess. She was then given a 20 minute break from interrogation. Afterwards, the same detective resumed the interrogation. This time he recorded it, opened with the Miranda warnings, and then once she had waived them he calmly led her through her earlier confession. All very camera-friendly and nice, but with repeated references to her earlier statements (he began with "We've been talking about this for a while...").
Unsurprisingly, Seibert confessed again. At the trial, she sought to suppress all of her statements. The trial court suppressed the pre-Miranda statements, but admitted the post-Miranda statements. She was convicted of murder, and appealed.
The US Supreme Court explained that the entire purpose of Miranda was to protect people's right against self-incrimination from the coercive pressures inherent in custodial interrogation. Previous to this, the totality-of-the-circumstances test was used to gauge the voluntariness of statements. The problem is that it's tricky for the court to really explore the circumstances of a stationhouse interrogation. Miranda made custodial interrogation easier... if a suspect was not warned of his rights, any statements were going to be suppressed. But if a suspect waived his rights, his statements were virtually certain to be admitted as voluntary. Not foolproof, but pretty good.
The courts have never asked for any particular phrasing of Miranda warnings, though. The test is just whether or not the warnings sufficiently inform a suspect of the relevant rights. But just like the courts have never asked for a particular rote phrase, they also don't afford any magic power to the warnings. The simple recitation of the words "you have the right..." doesn't render a warning valid if for some other reason it doesn't suffice. Such as where the manner in which the warnings are given is somehow calculated to circumvent a suspect's rights. Such as in cases where a suspect is coercively interrogated until she confesses, and then some warnings are glossed over and she is casually lead through the same confession.
Some lower courts described this sort of thing as "an end run around Miranda," and the Supreme Court agreed with them. Since the second set of incriminating statements were the direct result of the unwarned statements, and since the whole interrogation was essentially the same event with Miranda in the middle (as opposed to two distinct interrogations), the Court held that all of the statements were inadmissible.