The suspected schism in the association surfaced last weekend at its annual meeting in Perth when Mr Smith was replaced by Caroline Vass, its former vice-president and an East Lothian parent. Mrs Vass works for an educational publisher.
The association is continuing its fight over the Parental Involvement Bill, which plans to replace school boards `with more flexible parent forums and wants stronger opposition to the Scottish Executive reforms.
Mr Smith said that under its new president, the SSBA "may be not militant - because I don't believe Caroline will be militant - but more vocal".
A move to appoint Beattie Communications, a public relations firm, to represent the SSBA's position to the media had not been his decision, Mr Smith said.
Speculation about an internal split over the draft Bill surfaced after the Executive's press release announcing the consultation contained a quote from Mr Smith welcoming the fact that parents were being involved. But a press release from Beattie Communications quoted Mrs Vass warning that the new forums were in danger of becoming "moaning shops".
Mr Smith and Mrs Vass subsequently sent a joint letter to The TES Scotland expressing concern about comments over the SSBA's alleged "schizophrenic views" regarding the consultation.
Mr Smith repeated his belief at the annual meeting that school boards should be publicising their many successes and pressing the Executive to build on these. "I have always believed it is better to be inside the tent than outside it. My argument is that this is a much better way of doing things."
Mr Smith has been president of the SSBA for around five years, apart from a brief absence two years ago. He said he was likely to remain on the executive committee representing the Renfrewshire area until the end of the consultation period in June.
"My son leaves school in June anyway so maybe that will be the time to stop," he said.
Mrs Vass said after the meeting that the normal election processes had been followed. "We invited people to vote for the same president or another one."
Mrs Vass and Gordon Fairweather, the new vice-president, commented: "Our immediate plans are to represent our members and raise the profile of what we actually do. During today, we wondered whether civil servants and ministers have ever attended any school board meetings and if they realise what is happening out there."
They added that the new management team would be consulting widely with members. Mrs Vass said: "People were in total agreement today in their feeling that there is no reason to change things when they are working."
Earlier she told delegates: "Yes, we need more flexibility. Let's get rid of the elections and let's make it more flexible." But she urged school board members to "shout about the good things that school boards have been doing".
To the executive, she said: "This is not on. We need more detail here - more meat on the bones."
Members expressed a number of concerns about the proposals, including who would act as a national representative of the new parent forums, which could be set up along different lines in different schools to reflect different school communities.
Mr Fairweather said: "Boards and PTAs are engaging with each other. They have their specific roles and are working well and should be left alone to continue in that way."