The revelation came in the unexpected form of a talk by a senior north-east police officer to an Edinburgh conference on young people's life chances.
Chief inspector Harry Thorburn of Grampian Police said that having a school-based police officer in Northfield Academy in Aberdeen had proved "a runaway success" - although it was acknowledged that the public had been divided on its merits.
Since an officer was installed three years ago in a school which the chief inspector described as being "on the socio-economic margins of society", exclusions had fallen by 40 per cent.
The Executive and the Association of Chief Police Officers in Scotland are now5 considering whether to extend the practice nationally, the chief inspector said. Eastbank and St Mungo's academies and Whitehill Secondary, all in Glasgow, have already followed Northfield in having an officer on the premises.
Chief inspector Thorburn said that Northfield Academy was "a very challenging place indeed" but that the enthusiasm and commitment of those involved had been the hallmark of the project. It was not a cheap option, he stressed.
The Edinburgh conference was considering the extent to which education and skills could improve young people's life chances and prevent them offending. A number of speakers, including the chief inspector, lined up to offer suggestions on how different professionals could act as positive role models.
Referring to the 12 schools liaison officers Grampian Police has deployed since 1997, chief inspector Thorburn said: "Through our dialogues with the children, we have found strong evidence that police officers are seen as strong role models, particularly in areas where youngsters don't otherwise have much in the way of positive influences on their lives."
Teachers could also be role models for their pupils, according to James Cant, business development manager of Skillforce Scotland - but they would have to take part in extra-curricular activities if they were to have any chance of success.
The work being pioneered by Skillforce with North Lanarkshire Council on delivering an alternative vocational education programme for S3 and S4 pupils is being taken up by three other authorities next session. Dr Cant said that teachers had the same potential to be role models as the former services personnel Skillforce uses as instructors. They "can walk quietly into the classroom because they have a natural presence".
But Dr Cant argued that teachers had lost this possibility because they had cut back on extra-curricular activities. "It is important to give them back this potential," he said. "Extra-curricular activities turn schools from a two-dimensional into a three-dimensional model and allow teachers and pupils to see each other in different lights."
But there was a warning from David Eaglesham, general secretary of the Scottish Secondary Teachers' Association, that teachers faced walking a fine line between acting as role models for pupils and indoctrinating them - citing the case of Miss Jean Brodie and her "gels".
One way of ensuring that the right balance was struck was to make sure "the most suitable people" were members of the profession, Mr Eaglesham suggested. While the General Teaching Council for Scotland dealt with qualifications and registration, teachers had to be capable of "interacting with young people in very complex situations".
They should not stray into the professional territory of others, however, Mr Eaglesham said. "They should not take on other roles. They are not surrogate parents, or social workers, or police officers. There are huge differences between these roles."
"Going the extra mile" had its risks. Goodwill had to be balanced against the danger of "over-involvement" between pupils and teachers.
Steven Purcell, Glasgow City Council's education convener, also took up the theme of staffroom influence on pupils. "Teachers can be highly effective motivators and can have a hugely beneficial impact on the self-confidence, behaviour and enterprising attitudes which young people can take from school through to further education, training and employment - in short the 'can-do' attitudes which can give a young person access to economic and community participation."
But Mr Purcell said this needed a "clear understanding of the different styles of learning which work well with different children and young people".
There also had to be alternative approaches so that teachers had more than one string to their bow. "We have found in Glasgow, for example, that vocational education is welcomed across the board and that it can be particularly positive for young people experiencing difficulties."
For this reason there had to be a range of provision for young people experiencing difficulties and who may be at risk of offending. But, Mr Purcell said, "this range of provision needs to be organised into an effective framework of intervention".