"Bill has gone too far," one of them reportedly said.
But Bill McGregor was taking a relaxed approach this week, claiming that the HAS would be able to comment more freely now it no longer advises the management side of the national negotiating body for teachers.
He sparked fury among leaders of the Convention of Scottish Local Authorities when he was quoted in the media as saying that the 32 local authorities should be turned into seven or eight education boards, which would support schools more effectively. Mr McGregor was launching the HAS manifesto for next May's elections.
He said he regretted the way things had developed over the weekend, when Charles Gray, the education spokesman for Cosla, reacted by sacking the HAS from the management side of the Scottish Negotiating Committee for Teachers "with immediate effect".
One source said the HAS executive discussed 15 different alternatives to the current system, but did not favour a single one. Mr McGregor appears to have gone off on a tangent to give a personal view of the best option.
Mr McGregor had earlier told the HAS delegates: "We don't have a policy of getting rid of 32 local authorities. We understand there is no political commitment in the country for doing that. But the current system of organising education is not suitable for 32 authorities. There is a need for a simplified, stronger system which is still totally democratic."
Councillor Gray, however, reacted bullishly, writing to George Haggarty, the immediate past president of the HAS, saying: "As you will be aware, Cosla has written to you twice within the last five months, warning that continuing to criticise local government in the media was incompatible with your role as management advisers." He added that the association's "consistent disregard for the position of your local government employers leaves me with no choice."
Mr Haggarty tried to pour oil on troubled waters. Councillor Gray told The TESS that he had received a message from Mr Haggarty saying he wanted to "apologise and explain, because Bill has gone too far".
John Stodter, general secretary of the Association of Directors of Education in Scotland, said: "HAS can't be employed by local authorities as their professional advisers on the one hand, then in a different context argue for these very people to go out of existence."
The current debate, Mr Stodter said, was not about taking education out of local authority control and giving it a separate structure, but how to achieve integrated children's services. "The secondary heads appear to have missed that."
One HAS insider suggested that the headteachers had more in common with the Scottish Executive than either the unions or local authorities. When Peter Peacock was Education Minister, the HAS was "much closer to the executive, and we were encouraged by him to let him know about funding anomalies", said the source.