They did not hire a PR firm, and they did not call the police, despite what Hildy said. They first called their attorney. They also refused to cooperate with authorities. The "ransom note" was written in a handwriting suspiciously similiar to Patsy's. There were no actual signs of an outside intruder.
If John and Patsy Ramsey did not kill JonBenet, then she is still alive.
Interestingly, that retired detective who got involved in the case, with a terrific track record in solving crimes, believed the Ramsey's were innocent.