They clapped loud and long after a session in which the chief inspector stressed the need for good basic skills but also betrayed impatience with target-setting and appraisal - and advised them to throw away inspectors' reports if the didn't agree with them.
Mr Woodhead made his surprising suggestion to a head struggling to reconcile parents' demand for good 11-plus results with inspectors' complaints about too much stress on English and maths. "Who decides?" he asked.
"You do," replied the chief inspector, "the head and governors. And if you don't agree with the inspectors, put the report in the bin - I would."
Mr Woodhead was speaking at the annual conference in York of the Independent Schools Association, which includes the heads of about 300 smaller private schools.
Averil Burgess, who chairs the newly-merged service that is to inspect independent schools on behalf of the Office for Standards in Education, expressed surprise at Mr Woodhead's remark.
"I wouldn't approve of binning a report," she told The TES. "Any (inspection) report, whether you agree with it or not, is of value. I do believe in the virtue of the outside eye - and so does he!" Mr Woodhead, who was speaking after issuing a fighting statement expressing his determination to stay on in his job, was not asked any questions about his personal difficulties. ("Whatever we think about his private life, he's spot-on about education," one head said.) The heads nodded their approval as he stressed the importance of literacy and numeracy, of phonics, and of inspirational teachers with high expectations.
He urged them to raise their eyes to the horizon, beyond target-setting and appraisal, to an often idiosyncratic vision of the true purpose of education.
During his week's walking holiday in Wales, when not dodging the odd wandering paparazzo, Mr Woodhead revealed that he had been reading the biography of "Gorty" - Neville Gorton, a former head of Blundells, the public school in Devon.
As he recounted anecdotes about "Gorty" - dumping books and rushing onto the rugger pitch, gown flapping, to show sluggish boys how to push in a scrum - the chief inspector's eyes grew misty with reverence. "Gorty" would have put the national curriculum in the bin, he said. "Gorty" would probably never have passed his PGCE...
"No one else would have got away with it," one member of his audience remarked later. "It's pure Mr Chips."