Turing faced imprisonment after he was found guilty of gross indecency with another man in 1952, but avoided jail time by accepting injections of oestrogen to suppress his sexual urges.
The coroner recorded Turing's death as a suicide "while the balance of his mind was disturbed".
But rather than taking his life because of persecution, a lack of respect for his contributions to the war effort and being side-lined at the Manchester University computer department, Mr Copeland told a conference in the English city of Oxford at the weekend the genius took it all "with good humour".
This was supported by statements from Turing's friends to the coroner, who said he was in good spirits prior to his death.
The University of Canterbury professor told the BBC Turing was "hounded ... yet remained cheerful and humourous".
"In a way we have in modern times been recreating the narrative of Turing's life, and we have recreated him as an unhappy young man who committed suicide. But the evidence is not there."
Mr Copeland, who has several publications on Turing's work to his name, believed his death may have been accidental.
He said Turing often ate an apple before bed and did not always finish it.
Mr Copeland said medical evidence suggested he died from inhaling cyanide rather than ingesting it. Police had reported strong smell of the poison in Turing's lab, where he had used it for amateur experiments.
"The exact circumstances of Turing's death will probably always be unclear," Mr Copeland told the BBC.
"Perhaps we should just shrug our shoulders, and focus on Turing's life and extraordinary work."
Mr Copeland told the Daily Mail the inquest should be reopened.
"It would be a terrific thing to do," he told the paper.
"I think the nation owes it to Turing, in the Second World War he saved the nation."
During the war Turing contributed to the design of electro-mechanical machines (bombes) used to decipher Enigma, the code used by the Nazis to protect their radio communications.
When he was only 22, he created the Turing Machine, a mathematical device which was at the foundations of computer science.
In 2009 then-Prime Minister Gordon Brown issued an apology for the treatment Turing received following his conviction for gross indecency with another man.
Although under-appreciated in his time, the past weekend saw tributes flow for the great mathematician as June 23 marked 100 years since his birth.