Still troubled by the thought AS may not have been completely forthcoming.
I think it's likely JS sought advice from his mother, by phone or in person and gave her a version of events that did
not include murder, in the hope she would tell him what to do next.
Maybe just told her CM had disappeared and that no, he hadn't been to police yet.
AS, concerned the child was "missing" but also feeling an absolute parole -buster of a
headache coming on, may have advised JS it was in his best interests to get his side of the story across to police first and ASAP.
After the convoluted and generally botched way he disposed of the poor child's body, JS would have been strung out, exhausted, paranoid.
In that state, it seems unlikely the visit to Penrith police was his idea. Either they summoned him after KM reported her daughter missing or he went there on the advice of AS.
The strategy backfired when police seized his ute from the street while he was inside being interviewed.
As we know, in the hours/ days that followed after it became clear JS' verbal account didn't match up with the digital data of his movements (ute GPS and phone) and whatever the tyres/speedometer etc revealed.
The reason I think JS and his mother had a conversation of significance prior his first contact with police (and certainly before his arrest in Surry Hills), is because of what AS said in her daily telegraph interview.
She was so confident, so quick to declare police "should be looking at the mother (KM)" and cast her son as a patsy.
The minimising of his culpability and her authoritive tone implies she'd already formed a opinion of what happened based on JS' version of events.
I'm not in any way suggesting AS knew CM had died or that any crime had been committed at the time.
But it's possible police suspect there are people close to JS who are withholding information because they don't believe he is capable of "murder". Misadventure or accident, yes, but not cold blooded murder.
IMO it's the close confidantes, not the general public, Det Supt Doherty was addressing when he said police wanted to "clear up any ambiguity" about the alleged circumstances of CMs death.
Police want everyone in JS' circle -- (maybe even KM) to understand CMs death was unequivocally an act of murder, in the hope they'll reassess what they think they know.
All speculation, all IMO
Edited twice for clarity