This remarkable outbreak of amity took place at a four-day international conference in Edinburgh which attracted delegates from 26 countries to discuss quality assurance in schools.
They heard John MacBeath, professor of educational leadership at Cambridge University, say that Scotland was starting to "build trust" between the inspection regime and schools so that improvement and accountability can both be achieved.
And, in a further move towards consensus, Graham Donaldson, senior chief inspector, warned of becoming so preoccupied with evaluation that it might detract from the real focus of schools - what goes on in the classroom.
Mr Donaldson said: "We have to think very carefully about evaluation - how it's to be done, that it is done well, that it is part of the ongoing work of the school and that it does not prevent the school from realising its aims."
Both Professor MacBeath and Mr Donaldson agreed that "building capacity" to help schools sustain improvements was the key to making them effective.
Professor MacBeath cited a study in England which showed that no school involved had been able to keep up its improvements in test scores for more than three years.
He suggested that was because they concentrated their efforts narrowly on boosting attainment. The most successful schools were those that invested in "capacity building", which meant focusing on continuing professional development and quality of leadership.
Mr Donaldson stressed that Scotland took "a broad view of performance" and he hoped "persuasive ways" could be developed to measure the broader agenda of schools. But he added: "Scotland is not there yet."
HMI is to get tough new powers over underperforming authorities and schools, but Mr Donaldson played down the image of an all-powerful inspectorate. "What we seek to do in Scotland is to get the best blend between internal self-evaluation and external inspection."
On cue, Professor MacBeath agreed "blending" was important. "Research shows school improvement is not about external inspection versus internal evaluation or pressure versus support or top-down versus bottom-up changes.
It's not one against the other, but how you achieve the best blend."
Further agreement emerged on the importance of the inspected being able to get their own back. Mr Donaldson stressed that HMI subjects itself to evaluation involving teachers, parents and pupils. These independent surveys by outside consultants have shown "a high degree of confidence" in the inspection process.
Professor MacBeath commended this "reciprocity", while condemning the practice of "going into a school, going away and leaving behind a very angry staff".
Pressed in discussion how HMI could reconcile its claims to inspect and support schools at the same time, Mr Donaldson said it was not the dichotomy it seemed. The key was to focus on young people, he said.
"Inspectors don't go into schools to see that teachers are doing the kind of things that inspectors like to see, but to look at the experience of young people and how that might be improved.
"If we focus on young people, that is the bridge between what might be seen as the compliance agenda and the facilitating agenda. At the same time, we have to tell it like it is and report honestly on what we find."
Some delegates were curious to know what the effect of large classes was on quality assurance. Both men once again found themselves in agreement.
Mr Donaldson described class size as "almost an independent variable" and added: "We see very effective learning and teaching in small and large classes and we see very ineffective learning and teaching in small and large classes."
Professor MacBeath said that he had seen classes of up to 50 in Hong Kong and Singapore, while in African countries there might be more than 100.
"It's the effectiveness of helping children to learn that matters," he said.
Leader, page 24
* Evaluation is central to effectiveness.
* Internal and external evaluation make a powerful combination.
* Focus on what matters, which is learning in its broadest sense.
* Keep a sense of perspective about what can be achieved and how it should be done.