Look at it this way....some people have suggested that Burke hit her with a baseball bat and in panic the parents staged the death scene...if that were to have happen, by the time they thought out what to do and then stage the scene JBR's head would have been swelling and leaving enough pathological evidence that she was hit in the head before strangled.
You may be right. But not if she died within minutes of the head injury. It's the same argument being used about the ligature, that there was no head swelling b/c she died after being choked. Same argument here. If the blow killed her, no swelling.
I agree that I don't think it was a bat now. That should have left plenty of external bleeding and clearly didn't...no laceration.