I've wondered about that party, too.
FWI understand, possibly JB was hit in the head accidently, maybe by her brother who was only 9 at the time. Then everything that happened afterwards was a cover-up. Personally, I think that's the best explanation, except that I still can't imagine a parent garrotting a child, even if they thought she was dead. I've always thought they seemed to be protecting someone. Apparently, it was the strangulation that killed her, but the head injury may have made it appear she was dead. One thing I read said that she would probably have died from that even if she had not been strangled.
from everything I have read - the blow to the head was post-mortem.
she died from being strangled, she was alive as could be determined by the scratch marks around her neck as she was clawing at the rope.