If the Boulder authorities turn up solid evidence against Karr, I would agree with your sentence word for word. Otherwise, what I would say is the killer had to know the Ramseys and the house even if they didn't know him.
If the killer is a total stranger to the family and that house, and he picked JonBenet randomly, then the circumstances of the killing -- as they've been related to the general public -- are one long series of amazing coincidences.
Do you know where your neighbor keeps paint brushes?
Would you be able to get around your neighbor's house and find any of the items or similar information mentioned in this case? I wouldn't. I can't find stuff in my own house half the time.