Donaldson relatives reject claim he was killed by IRA on Adams' orders
Denis Donaldson's family have said they do not believe the Provisional IRA murdered him or that his shooting was sanctioned by Gerry Adams.
Ciaran Shiels, a lawyer for the family, met Garda Deputy Assistant Commissioner Derek Byrne and senior police officers in Belfast on Friday.
He told BBC Northern Ireland that the officers had provided an update on progress in their investigation.
Mr Shiels added: "The one theme that has come out of today's meeting is that the theory that was being advanced by BBC Spotlight earlier this week - that this was in some way carried out by the Provisional IRA or authorised by Gerry Adams - I think that it's absolute nonsense.
"It does not marry in any way with the lines of inquiry progressed by the guards (Garda) or by the (police) ombudsman."
Gardai investigating the murder have already ruled out any involvement by mainstream republicans.
Intelligence gathered by the PSNI has also ruled out Provisional IRA involvement.
This information was passed to gardai investigating the case, who have always focused on dissidents.
A reliable security source in Northern Ireland said there was surprise the BBC Spotlight programme made the allegation.
"No one, and I mean no one, on either side of the border believes this claim has an ounce of truth in it," he added. "The guards say it's nonsense and the PSNI believe the same. The so-called Real IRA did this."
Mr Donaldson was killed by a shotgun blast in April 2006 as he opened the door to his remote Donegal cottage. He was in hiding after being outed as a British agent of nearly 20 years.
A spokeswoman for the BBC said: "The BBC stands by its journalism."