Well, that's a surprise to me. I'm no expert but the autopsy report (which is online and you can google it) specifically states that the skull was split wide open from front to back along the top right side. The coroner also stated that it was the skull injury that caused the death, not the ligature. He even goes on to say that the ligature was applied 10 - 45 minutes AFTER the head injury was sustained.
So, I don't know what you've heard but that's what the autopsy report said.
Read it again, please. The first page summary states cause of death as asphyxiation from strangulation. Just above the ME's signature.