I don't believe anyone deliberately murdered JonBenet. I believe she died as the result of an accident, probably a late-night argument with her brother as they were both in the kitchen eating pineapple when the parents thought they had gone to bed. Or, that Patsy, frazzled by the holiday events and trying to pack for an early-morning cross-country move to their vacation home, snapped and slapped JonBenet for another soiling incident, and JonBenet hit her head on something, and died.
What I DO believe was deliberate was the cover-up. They were just too image conscious, too fanatical about prestige, images, etc., to be exposed as a dysfunctional family or to let their child Burke go through the wringer as even an accidental killer. I believe that Patsy put the elements of cover-up in place and by the time John came down and realized what was happening, the train was gaining speed and he just acquiesced. Clearly reluctantly.
That they were trying to jet out of town, that he was heard by a police officer exhorting their pilot to get ready to fly out of town (until the officers stopped that) when their child was lying cold on the floor next to their Christmas tree, shows a guilty mind. What innocent parent would leave their child's death scene for someplace 1,000 miles away within hours of her "attempted kidnapping" rather than stay on the scene and urge the police investigation onward?
There are just so many telling elements. The blanket over the child; only a person close to a victim does that. The attempt at a garotte to cover up the true cause of death. (The "sexual assault" evidence could easily have been a combination of nappy rash due to her soiling/wetting and self-exploration).
Burke has probably repressed the memory and convinced himself he was not responsible. I think it Patsy had lived she would have eventually slipped but took the secret to her grave and we can see John is not the type.
I really could curse those stupid police officers who failed to take elementary steps to separate the family members, keep the crime scene clean, call for expert assistance and not be bowled over by wealth and a stately house.
Read the Ramsay's book, "Death of Innocence," and you'll get what I mean about their mentality. Every single page drips with narcissism, an obsession with public image, and drama.