Speaking at the Leveson Inquiry today (June 11), Brown repeated his rejection of claims by The Sun that the source for its story about his son Fraser was an individual who had a family member with cystic fibrosis.
While he denied the suggestion that Brown's son's medical records were hacked, chief executive of NHS Fife John Wilson said: "Any breach of confidentiality in the NHS is unacceptable.
"We now accept that it is highly likely that, sometime in 2006, a member of staff in NHS Fife spoke, without authorisation, about the medical condition of Mr Brown's son, Fraser."
He continued: "With the passage of time it has not been possible to identify all the circumstances. We believe, however, that there was no inappropriate access to the child's medical records.
Wilson added: "In the six years which have passed, NHS Fife has tightened up its procedures on patient confidentiality, and staff have had appropriate training.
"I have apologised to Mr and Mrs Brown and we have taken steps to ensure that what happened to Mr and Mrs Brown and their family should not happen again."
Brown had previously suggested that medical records regarding their son had been obtained and were the source for the story in question.
The Sun later added in a statement: "We are able to assure the Brown family that we did not access the medical records of their son, nor did we commission anyone to do so.
"The story The Sun ran about their son originated from a member of the public whose family has also experienced cystic fibrosis.
"He came to The Sun with this information voluntarily because he wanted to highlight the cause of those afflicted by the disease. The individual has provided a written affidavit this afternoon to a lawyer confirming this."