The move was "a regrettable sign of the times", Maire Whitehead, the association's vice-president told The TES Scotland. But the Educational Institute of Scotland believes a blanket policy is unworkable and unhelpful.
Mrs Whitehead, headteacher of St Mirin's primary in Glasgow, says most of those accused are exonerated but "mud sticks". Members' homes have been plastered with graffiti and others have had to move. Some have retired because they cannot carry on.
The AHTS, which represents just over half of primary heads, is advising them "not to permit any occasion when any child is alone in the presence of a single adult".
It admits: "This is going to cause operational difficulties in many schools. Please remember, however, that even a three-year-old can unwittingly cause a great deal of difficulty for a school, its community and members of staff."
The EIS says it has not issued blanket advice precisely because of these difficulties. Ken Wimbor, the union's assistant secretary, said: "There are many instances where guidance staff in particular or headteachers want to have confidential meetings with pupils on delicate matters where they would not want another adult present. So we prefer a pragmatic approach based on teachers' common sense and a knowledge of their pupils."
Mr Wimbor acknowledged that allegations against teachers are on the increase, although the evidence is largely anecdotal. Following a recent case where a music instructor in North Ayrshire was found guilty of five charges of indecency involving pupils other instructors, whose job involves one-to-one sessions with pupils, had raised concerns that they could be falsely accused, Mr Wimbor said.
The Headteachers' Association of Scotland, representing secondary heads, has not formally discussed the issue. "It may be an unfortunate necessity," Jim McNair, its secretary, conceded. He believes pupils should be approached with caution only where there are particular suspicions.
Mrs Whitehead said the AHTS had been forced into issuing guidance. "We didn't want to do it and we recognise that it will be impossible to follow at all times." But she said it was the advice she has given her own staff over many years, particularly for male teachers who are often vulnerable to "daft girls".
The association says teachers may well have become victims of schools' success in imparting "don't go with strangers" messages. "Coupled with exhortations from the media and school staff that children need no longer keep unsavoury secrets to themselves and to report 'suspicious' things to an adult, all this can have the effect of causing irredeemable damage to an adult's career," Mrs Whitehead said.