Good points all. This case is maddening; something contradicts every scenario I can come up with. I still feel an intruder theory is impossible, so am speculating strictly within some kind of RDI boundaries.
BDI offers the best explanation of why Patsy penned the ransom note and both parents covered up. Possible motives include jealousy over JB's beauty pageants and the accompanying bulk of parental attention it accorded her. Also we have the unclear nature of Burke's possible learning disability, as well as the prior incident with the golf club, which may indicate a brewing rage towards his sister. Finally, Burke's reaction to his sister's death was really bizarre. It stood out, even amidst his parents' puzzling behavior.
JDI explains perhaps the incredible number of doctor visits for JonBenet, all seemingly concentrated around the genital area, as well as Cyril Wecht's early conclusion that the autopsy indicated chronic sexual abuse. Then there is the curious tibdit about the dictionary being left open and pointing to a definition of "incest." However, as has been noted many times before, how likely is it that Patsy would have helped cover up her husband's sexual abuse and murder of their daughter?
PDI has a lot going for it. Patsy's behavior was strangest of all; wearing the same clothes, peeking out between her fingers at the police, the strange, detached public statements about "that child," etc. And, of course, the ransom note, in my view, ties her into the crime in some way. I think it's the strongest piece of evidence in the case, and her personality is written all over it. However, the record also indicates she was a loving mother who was very involved in JonBenet's life. So again, contradictions....
The whole strangulation scene, garotte or not, is hard to fathom when the fractured skull is factored in. It's like two different versions of death; since JonBenet couldn't be murdered twice, at least one had to be staged. But I just can't imagine any parents staging either one. The only thing that could perhaps make sense is if her head was smashed against something as she was being strangled. But then, I can't picture any of the three in that house doing something like that. So....
It's back to square one, I guess. Since Patsy is gone, and John is unlikely to ever tell the truth, the only chance we ever have at finding out exactly what happened, imho, is if Burke ever decides to talk about it. That's almost as unlikely, though, and he may not even know everything.