Members of Clyde Valley Flute Band from Larne wore Parachute Regiment insignia with the letter ‘F’ on their shirts during Saturday’s parade.
Police said an agreement had been put in place before the march, and officers flanked the band during the parade.
But governor Graeme Stenhouse said he has no knowledge of such an agreement.
Thirteen people were shot dead when members of the Army’s Parachute Regiment opened fire on civil rights demonstrators on Bloody Sunday in Derry in 1972. A 14th person later died of their injuries.
A former British paratrooper, known as Soldier F, is to face a court in Derry next month to be prosecuted for two murders and four attempted murders over Bloody Sunday.
Mr Stenhouse said in meetings ahead of Saturday’s march the association was not “asked to give any assurances as far as I can remember”.
“And we certainly wouldn’t have given any,” he said.
PSNI Supt Gordon McCalmont told BBC Radio Foyle on Monday an agreement had been reached on contentious symbols before Saturday’s parade.But Mr Stenhouse added: “We had a meeting with senior PSNI officers from Strand Road and there was no agreement made by us.
“Well, having spoken to fellow senior officers, they are unaware of any agreement being made at any meetings.”
On Saturday, PSNI officers escorted Clyde Valley Flute Band during the parade and their bus was later stopped by police.
The Apprentice Boys described the police’s actions as “heavy handed”.
But Assistant Chief Constable Alan Todd said the response was “proportionate, responsible and constructive”.
Police later stopped the band’s coach after it left the city to take down the names and addresses of the band members.
The Parades Commission said it had received a number of complaints regarding the Apprentice Boys parade.