Prosecutors say it's not and the evidence points, beyond reasonable doubt, to her boyfriend Ricardo Barbaro being behind a tirade of violent abuse that resulted in two significant plunging knife wounds.
Ms Price's body was found in the bedroom of her South Melbourne apartment on May 5, 2020 but it's alleged she was killed in the early hours of April 28.
But Barbaro's barrister say it's telling that there was no motive put forward by the prosecution during three weeks of evidence in Victoria's Supreme Court.
In closing arguments to the jury, Rishi Nathwani, pointed to another man, Mark Gray, who was infatuated with Ms Price, asked a mortician to make her look "hot" after she died and had been spurned by her for people like Barbaro.
Mr Gray referred to himself as being "always the bridesmaid, never the bride" when it came to Ms Price, who tried to extort him for $100,000 over a false rape allegation.
"He had the motive," Mr Nathwani told jurors.
But Damien Hannan, for the prosecution, said Mark Gray - the owner of several brothels who was in denial about being Ms Price's sugar daddy - was a distraction for jurors.
A suggestion that Mr Gray was an alternative suspect to Barbaro, and that he may have hired a hitman in response to the extortion attempt, was "ridiculous", he said.
He pointed to evidence of Barbaro's blood under Ms Price's fingernails and his fingerprint on her bedroom mirror.
But Mr Nathwani said jurors should re-examine the evidence of the forensic scientist who said he couldn't say for certain it was Barbaro's blood.
Mr Hannan said somehow Mr Gray would have to have hired an "Einstein hitman" who knew there was blood everywhere, injuries to both Ms Price and Barbaro, and that Barbaro would act consistent with guilt after the murder.
Barbaro was arrested interstate several days after the murder, with prosecutors alleging he drove Ms Price's car to a property in Diggers Rest before travelling to the ACT.
"A tremendous set of coincidences or a very, very smart hitman - it's ridiculous, isn't it," Mr Hannan suggested.
For dismissing Mr Gray as a distraction, Mr Nathwani noted that Mr Hannan had spent 35 to 40 minutes of his hour-long closing address talking about the man who had never even been investigated.
"We say this investigation has been blinkered with subconscious bias - starting at the end and working backwards," he said.
"We ask you, on behalf of Mr Barbaro, to forensically scrutinise everything and please do not do it as superficially as police and the prosecution have."
He said CCTV footage of Barbaro and Ms Price on the day of her alleged murder demonstrate she was happy to be around him, and pointed to multiple pictures of him in her bedroom.
"She was happy to be, and wanted to be in the relationship with him," he said.
Mr Nathwani's closing address is set to continue on Wednesday, before Justice Lex Lasry addresses jurors and they begin their deliberations.
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