You said it yourself...anything is possible. I'm only saying that whoever did it (Karr or anyone else), it wasn't an instance of some transient blindly happening upon that house with that little beauty queen. Whoever wrote the ransom note did not just channel the amount of John Ramsey's bonus.
So if it was Karr, I would expect to eventually hear he had some connection to the Ramseys, even if they were unaware of it. For example, suppose Karr (or whoever killed JonBenet) was hanging around kiddie beauty pagents, became obsessed with her, and began quietly stalking her. The killer might then have acquired sufficient information about the family to do the things we have been told are facts in this case.