Dr Sandra Lean said the man left a used condom yards away and lived in a house overlooking the path in Midlothian woodland where 14-year-old Jodi’s body was found.
Jodi’s then boyfriend, Luke Mitchell, 14 at the time, is serving life in prison after being caged for the gruesome 2003 murder but questions remain regarding his conviction.
Dr Lean told James English’s Anything Goes podcast of the mystery man: “His story is he went down the path that night to masturbate because he didn’t have any privacy because he shared a room with his brother.
“He did what he did, discarded the condom and then came back up again. If that was correct he would virtually have to step over the body on the way down and on the way back.”
Dr Lean accused police of botching a probe into the alleged confession in Dalkeith, Midlothian.
She said poring over the case files has led her to believe there were at least three other suspects aside from Mitchell.
Dr Lean said her interest in the case was spurred to ensure her teenage daughters’ safety who at the time went to the high school close to where Jodi’s body was found.
Mitchell claims police cornered him in the bathroom and tried to force him to confess to Jodi’s murder.
Dr Lean, who led a series of failed appeals for Mitchell, said the mystery man believed he was out between 8pm and 9pm on June 30, 2003. Jodi died at around 5pm.
She told the podcast that detectives “messed up” tests and did “nothing” over the claim as it came three years after the killing and the case was closed.
Mitchell was jailed for 20 years in 2005 though campaigners point to him passing a lie detector test as further evidence of his innocence.
He lost an appeal against his conviction in 2006 and an appeal against his sentence in 2011.
But police chiefs are “satisfied” they have the right man and are not looking for anyone else in connection with Jodi’s murder.
Detective Chief Superintendent Clark Cuzen said: “Following the discovery of 14-year-old Jodi Jones’ body within a wooded area in Easthouses, Midlothian, on 30th June 2003, a thorough investigation was conducted by Lothian and Borders Police.
“Extensive forensic analysis was carried out along with door-to-door inquiries and other investigative techniques and a full report of the circumstances was submitted to the Procurator Fiscal.
“As a result, Luke Mitchell, who was 15 at the time, was charged with Jodi’s murder, before being convicted and sentenced in 2005.
“We are satisfied that we do not need to trace any other individuals in connection with this investigation.”