"Finally got em" but did they?

After nearly ten years of lawsuits and investigations and media appearances by the Ramseys and all associated with the case, Patsy Ramsey died of ovarian cancer on 24 June 2006. Two months later, on 16 August 2006, John Mark Karr was arrested in Thailand for the murder of JonBenet Ramsey, following a four-year exchange of emails with a journalism professor at the University of Colorado. He was extradited to the United States to face the murder charges.
Karr gave a long and detailed confession of how he committed the crime and actually tied up many loose ends that had puzzled investigators. In particular, he claimed he had actually been in the house for many hours before actually taking JonBenet from her bed, therefore he had plenty of time to draft and write a ransom note. Karr, also arrested on child pornography charges, claimed that he was in love with JonBenet and had asphyxiated her for sexual reasons, in the process accidentally killing her. He then hit her on the head to make sure she was dead, so that she would not wake up brain-injured. Karr also claimed to have previously met and befriended her, although he was cagey as to the exact nature of this meeting, thus explaining why there had been no signs of a struggle.

The charges against Karr were dropped after it was determined that the DNA recovered from JonBenet’s underwear did not match that of Karr. Moreover, there were many inconsistencies between his exhaustive account of what had happened and the physical evidence at hand. It was implausible for the girl to have sustained her injuries if what Karr said happened actually did take place.
After the charges were dropped in the Ramsey case, Karr was extradited to the state of California to face child pornography charges. He was released once again due to the investigators losing his computer that would have provided the evidence needed.
The murder of JonBenet Patricia Ramsey remains unsolved.