Yes, we do know that it was the cause of death. It's listed on the autopsy report as the cause. She had petechial hemorhages on her face, eyelids, eyes caused by it. Yes, her head was also bashed in, but craniel trauma doesn't cause petechial hemorhages, strangling does.
You may be right. We discussed that earlier but many, including people in that profession, interpreted the cause of death as being from BOTH strangulation and head trauma. They seem to think that the coroner's report was inconclusive about it. The relevant quote from the autopsy report was posted a ways back on this thread, but it states that both were causes of death.
The cause of death as listed in the autopsy report was:
"Cause of death of this six year old female is asphyxia by strangulation associated with craniocerebral trauma".
Many pathologists have interpreted that as, "he didn't really know for sure which, or if both, actually caused death".