Three years ago, the authority became concerned after several of its schools expressed anxieties about the unnamed inspector.
The schools claimed that the inspector had wrongly warned them that they risked being judged as "failing" - only to emerge with clean bills of health in the final report.
The authority complained to the Office for Standards in Education about the stress for staff. It also sent one of its own senior inspectors to talk to the inspector during a school visit.
OFSTED responded by writing to Keith Mitchell, Durham's director of education, rejecting the original complaint and registering Mr Woodhead's "serious concern" about the intervention by the authority's own inspector.
The authority pursued its complaint, through OFSTED's internal procedure, and, not having success, took its case to the external adjudicator, Elaine Rassaby.
She found that OFSTED could have investigated the original complaint more fully and concluded that OFSTED's letter had been inappropriate in making reference to Mr Woodhead. "The reference to the chief inspector' view of this matter was unwarranted and implicitly threatening to the complainant," she found.
A year after this verdict, Mr Woodhead wrote to Mr Mitchell. He said: "OFSTED and I accept that my comments should not have been expressed ... and apologise if they were interpreted as being threatening.
"We have accepted the recommendations of the OCA (adjudicator) and our practice now adheres to her recommendations."
However, Mr Mitchell remains unsatisfied because Mr Woodhead was never interviewed about his role in the complaint. Ms Rassaby admitted that she had not questioned Mr Woodhead.
School standards minister Estelle Morris advised Mr Mitchell to take the matter up with the Parliamentary Commissioner for Administration. However, when he did, the commissioner said the issue was not within his jurisdiction.
In a letter to this week's TES, Mr Mitchell writes: "Where is OFSTED's accountability? Where lies accountability for the chief inspector's personal conduct?"
An OFSTED spokesman said: "We accepted the adjudicator's point. However, the reason our original letter was sent was over a very serious case of interference by the education authority in the independent process of inspection."