Paul Igoe, who is accused of murder alongside his sister Caroline Igoe, was alleged to have made the comment to a friend on the day 26-year-old Mr Barclay died.
But in his closing speech at the High Court in Edinburgh, defence advocate Gordon Jackson, QC, asked the jury to dismiss the evidence.
He said: "There is a pattern in what he said – drunk, wrong story, nobody believes him, eejit."
Mr Jackson also said that for someone to use the murder weapon they would need to be familiar with it before it would work and added Paul Igoe, 37, had "no link to the gun whatsoever".
Caroline Igoe's defence solicitor advocate, Jim Keegan, QC, said suggestions his client was a "callous killer" were the "stuff of pure fantasy".
He said the only thing the 32-year-old was interested in before her boyfriend Mr Barclay died was becoming a cheerleader and getting on the catwalk.
The court has heard Ms Igoe and Mr Barclay, 26, had rowed over the phone in the hours before his death because he had gone out drinking.
Mr Keegan said the prosecution alleged that Ms Igoe unpacked the gun in the street and shot Mr Barclay in full view of residents.
He said: "The Crown case is she unpacks it in the street and shoots him, and she shoots him in full view of the street.
"How likely is it that he stands there and waits?
"The Crown are asking you to accept the only one that uttered anything was Martyn Barclay, who called out her name twice.
"Not only is she a callous killer but she is a silent killer.
"That is the stuff of pure fantasy, and apparently because they fell out over her desire for him to get home early."
Mr Keegan pointed to evidence about a car journey in which the court heard Mr Barclay said he had a gun.
He said: "He said his lifestyle meant he needed a gun.
"The only thing Caroline was interested in was becoming a Score Angel and getting on the catwalk right up to 17 January."
Ms Igoe and her brother deny murdering Mr Barclay by shooting him in the head at Hazelwood Grove in the Inch, on 17 January last year.
Lord Bracadale is expected to finish summing up to the jury today.