He said the"dynamics"of the family were vital to the investigation.
But it was critical for people making claims and comments on social media about the relationship to contact police to help build a full picture for the coroner.
"Coronial issues like this have the ability to drive reform amongst issues like domestic and family violence,"he told media on Thursday afternoon.
"If there are people out there making the comments ... then please come forward and substantiate those claims.
"I would even go so far as to call it an impassioned call to the public."
Loading
Ms Clarke,31,and her three children – Aaliyah,6,Laianah,4,and Trey,3 – were on the school run before 8.30am on Wednesday and had just left her parents'house in nearby Durimbil Street.
Senior police believe Baxter had a container with an accelerant,reportedly a jerrycan filled with petrol from a local service station,anddoused the car while he was still inside with his family.
As the car burned and Good Samaritans,including neighbours and nearby tradesmen,ran to help,Baxter took his own life.
Matt Gee-East will never forget the moment he and his brother tried to stop the rolling,burning car and saw the three children inside.
"[Ms Clarke] was just screaming out for help and then said that her babies were in the car,"he told Nine News.
Inspector Thompson said Baxter's death was not"suspicious"but the cause of death would be confirmed in the results of a post-mortem examination.
Police converged on his Carindale home on Thursday and are not searching for any other parties.
The Camp Hill tragedy highlighted that some people were"suffering in silence"under the"scourge"of domestic and family violence,with support services often seeing requests for help surge after such incidents,Inspector Thompson said.
"I understand the myriad of complexities around that and why people can't come forward or don't come forward,but we continue to encourage that to happen".
Loading
Police statistics show a total of 30,796 domestic violence protection orders werebreached last year,almost five times the 2001 figure.
Women's legal groups have said although the increase could mean more women are seeking and receiving help,breaches are likely to still be under-reported due to difficulty getting police to take action.
If you or someone you know needs help,support is available at Lifeline on 13 11 14,Beyondblue on 1300 224 636,or 1800 RESPECT.