Now Highland councillors are to seek the help of MSPs to establish beyond question the extent of Sir Stephen House's powers and what safeguards are in place in relation to the policy.
It follows Highland Council voting by an overwhelming majority to call for Police Scotland and Chief Constable Sir Stephen to review the decision.
Skye councillor Drew Millar who chairs the council's Safety, Public and Engagement and Equalities Committee, wrote to the Scottish Police Authority (SPA) of councillors' concerns that the policy had changed without public debate of consultation, saying "such a radical change in policing surely must be considered by the SPA and parliament"
In his reply Vic Emery, SPA chairman, said he did not accept that "a material shift in policy" had taken place.
But he added: "I do think it would have been helpful for communities and local councillors to have been made aware of these changes at an earlier stage, and for more information to have been provided on how the standing firearms authority works and what it means in practice."
In a separate letter to the depute leader of the Highland Council, Black Isle councillor David Alston, Sir Stephen explained how he had come to his decision.
The chief constable said: "I can nevertheless give an undertaking to take into account Highland Council's motion, the next time the standing firearms authority is reviewed by the Armed Police Monitoring Group.
"In doing so I do not want to create unrealistic expectations, but I can confirm the council's view will be registered alongside the range of intelligence, threat and risk assessment and will be considered."
Mr Alston, who has been outspoken in his criticism, has said he fails to see the need to change the current practice, in which officers keep weapons in a secure cabinet in the armed response vehicle and only take them out when it is deemed necessary.
He said "It is clear from the letter from the chairman of the police authority that there is a recognition that perhaps the chief constable has not handled this particularly well in PR terms; and that there should have been greater transparency.
"But it is equally apparent that nothing will change. The authority still accepts it is an operational matter for the chief constable.
"It is also clear from his letter that Sir Stephen is not willing to entertain the idea of regional variation of the standing authority. "