They both went to great lengths to keep Burke out of it. Patsy claimed Burke was sleeping. We know there's proof that's a lie. The most important words to listen for when someone is making a confession is when they say they or someone else was asleep when the crime took place. They do that to distance the person from the possibility of committing the crime. There's no way Burke could have committed the crime if he was asleep? Since you can't place the person away from the scene, the next best thing is to say that they weren't even conscious when the actual crime took place. It's also a way to tell others that since this person wasn't awake when the crime happened, there's no reason to question him because he doesn't know anything period, didn't see nor hear anything. I think both parents did their separate things. Patsy started on a ransom letter and John went to stage a killing. Poor parents though, she wasn't even dead yet, they could have saved her life if they had driven her to the hospital. Patsy's words on the RN. Foreign factions don't use American high society slang. John's boyscout's garrote. Foreign factions don't learn that garrote in guerrilla scouts;every country I've been to has had their own way of tying rope, believe it or not; subtle differences. That's why the crime was half kidnapping and half straight up murder. PR called the police to report a kidnapping for ransom and never looked over to the phone again for the rest of the day. She knew they had the money to pay it. They'd pretend to pay the ransom without getting JB back. This would clearly clear them. JR hid the body and locked the cellar door. I'm not sure if JR knew that PR called the police yet at this point. If he did, he too wasn't thinking clearly. I don't think they thought the police were going to be there all day. He might've gotten nervous. What if there was a smell? What if they decided to question Burke thoroughly? He had to make sure he had control over the finding of the body and that nobody needs Burke's help to find his sister.
It wasn't just about saving him from jail, public scrutiny, etc. JR/PR grew up in an era that feared mental institutions where in their haydays we're performing lobotomies and other progressive treatments and experiments. It was a place you went to and got worse, and died there. Families put their would be autistic children in there. A very small number of mental institutions were still running by 1996. They didn't want him taken away and placed in a ward. Many people formed the opinion that Burke is on the autism spectrum, from watching his interview. I'd say the Ramsays did the right thing. They cheated the system and it worked. Burke grew up to be a rather peaceful child.
How would this have played out if the Ramsays were not rich and influential? If this had happened in a crime ridden area? The police would've all looked at them suspiciously and no one was going to "clear" them of a crime scene that had all three of their DNA in it.