You can doubt it all you want. But why would the parents not call for an ambulance, if they had come across an unconscious JBR with no bleeding from her scalp, maybe some swelling, but not knowing how bad her injury was? I'm not buying that. I believe PR found her already dead and they had to come up with the random letter to try and explain what had happened. They then followed the "don'ts" of the ransom letter as if to achieve the "beheading" of JonBenet, which, if it worked, they could claim they were so upset that they didn't know or realize what they were doing.
There are probably parents so evil that they could murder a child and rationalize it, but I don't believe that JR or PR is that evil. I think they did what they did to save Burke, since JonBenet was already gone. They made that decision so they didn't lose their remaining child.
It has been speculated ad infinitum on these threads why the parents didn't call for medical help. They were trying to protect BR is a popular theory. And as parents i think they knew how dire the situation was with their daughter when she received that potentially fatal head injury. And when exactly was that RN written? Before or after the fact of JBR's death? I don't think we know that for a fact do we?
But i think we could say the RN was definitely written to give a certain perception of what this crime was trying to point to. Even though the RN was an epic fail because of its absurdity.