In handing down her findings on Thursday, Deputy State Coroner Elizabeth Ryan said she could not make any recommendations to improve the level of care given to William Rodney Cahill who suffered from severe long-standing schizophrenia before the unprovoked attack.
Mr Liston, then 51, was attacked by Cahill while standing at a bus stop in the Sydney suburb of Camperdown on December 10, 2015.
At about 8.30pm, Cahill came out of his building, walked towards Mr Liston and started swinging a 15cm kitchen knife. After yelling "why are you doing this?", the teacher fled but tripped over the median strip and was stabbed multiple times.
He later died at Royal Prince Alfred Hospital from a stab wound to the heart.
At the inquest, Ms Ryan was charged with determining whether the level of care offered to Cahill by a mobile assertive treatment team at the Camperdown Community Mental Health Centre was sufficient or whether it could have been improved to prevent the attack.
"In the grip of a psychotic episode, Mr Cahill used extreme violence at a time when he was in their care. The consequences were devastating," she said on Thursday.
With Mr Liston's partner Maggie Jones watching via video link at Lidcombe Coroners Court, Ms Ryan found the medical team provided Cahill with the kind of intensive care and support that he required.
"There was no deficiency in the care which was provided to Mr Cahill ... either at an individual or a systemic level," the coroner said.
"On the contrary, the support which this service supplied was of a high level and was provided by clinicians who were both competent and caring."
Psychiatric evidence given in the inquest was acknowledged, with Dr Danny Sullivan saying the stabbing was "an unpredictable outburst of homicidal violence which was directed at a stranger".
The chances of such an event occurring were one in several million, said Associate Professor Matthew Large, who described the killing as "an event that (was) as rare as it (was) terrible".
Although Cahill showed occasional moments of delusional misidentification where he would think a person was somebody else, he was not persistently aggressive.
He was also his normal self in the days before the tragedy and did not show any signs pointing to the impending outburst.
Cahill had been charged with murder, but NSW Supreme Court Justice Geoffrey Bellew found in October 2017 that he was not criminally responsible for the killing because of his mental illness.
The judge ordered Cahill be detained in an appropriate correctional centre or mental health facility.
While evidence showed a gap in that individuals like Cahill could not be subject to involuntary detention in 2015, the coroner said making a recommendation about this was outside of the scope of the inquest.
"However, it is a matter which deserves serious consideration within the community, and amongst health care services and those who provide their funding."
In closing her findings on Thursday, Ms Ryan acknowledged the devastating impacts of Mr Liston's unexpected death.
"Brian's death was shocking and profoundly sad. He was deeply loved and is deeply missed by his family and his many friends," she said.
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