I used to be a full on "PR did it!" supporter, but when you think long and hard about it, it doesn't really add up. If it's an accident, you call the police. If PR or JR is the intentional culprit, there's just no compelling rationale for why they cover for the other. Again, you call the police.
The only way they work together crafting a ransom note and staging the elaborate kidnapping is if the risk (being caught covering up a murder) is worth the reward. What could that valuable reward be, except for the protection of their other child.
A BDI theory is the only one that really makes sense. He kills JBR and the parents realize that his life is now ruined. This one act has taken both their daughter AND their son away from them.
Panic sets in and suddenly the idea of being able to save their child from prosecution doesn't seem so crazy. If there's an outside chance that the charade will work, the R's decide to risk it so that they won't lose their son and he can have a shot at a 'normal' life.
Suddenly all the evidence makes sense. It is just a smokescreen. If the R's did do it, this is really the only logical explanation for the whole entire ruse.
I have never seriously considered BDI because I found it inconceivable that a child his age would do it but for the first time I am looking at it. What you say makes sense. I disagree that the parents would not cover for one another but the strongest case can be made for them teaming up to protect their only remaining child. Considering it more in depth, if BR had merely inflicted the head bash, I believe the parents could/would have called an ambulance for their daughter and it could have been claimed to be an accident. If, however, BR strangled his sister to death with the garotte, there is no way that can be claimed to be an accident. Anyone seeing that would consider it purposeful murder. In THAT case I can see the parents teaming up and creating the foreign faction ruse to protect their son. That is the only way I can see it.