The Charities Bill proposes that they should be regarded as charities only if they pass the test of whether they provide a "public benefit" - a concept that appeared to baffle both sides of the argument.
In the course of the exchanges, it emerged that nobody has a very clear idea of how much independent schools receive in tax breaks. The major concession is rates relief, which Judith Sischy, director of the Scottish Council of Independent Schools, agreed stood at around pound;2.5 million.
That was "a reasonably accurate estimate", Mrs Sischy said. But the Scottish Executive suggests the figure could be as high as pound;4 million, which Mrs Sischy felt was a "guesstimate". The only other main benefit was gift aid on donations made to the school.
Mrs Sischy and three of her colleagues put up a stout defence, claiming that independent schools are of public benefit and maintaining that they would become more exclusive if they had to put up fees.
Mrs Sischy said trying to define what public benefit accrued from having a private education was "invidious and difficult".
John Stoer, headteacher of St Aloysius' College in Glasgow, told MSPs: "I have been teaching for 27 years, all bar one term of which has been in the state sector. As a headteacher of an independent school, my aims now are the same as they have been throughout my teaching career.
"What my colleagues, not just in school but in the profession, and I have done has been for public benefit. I find it hard to understand how good education could be a disbenefit, because good education is to the public benefit."
Janet Allan, principal of Donaldson's College for the Deaf in Edinburgh, wondered what was meant by "public" - everyone in the public or a sector of the public? "My school benefits a small section of society hugely - it is a section that no one else in Scotland is capable of educating.
"There is a problem with what the term 'the public' means. Do we have to benefit a certain proportion of the public?"
Patrick Harvie, the Green Party MSP from Glasgow, challenged the witnesses to consider the disbenefits. "The argument is that to provide the opportunity for a separate system of education that is easily accessible to people who are very wealthy and that is not easily accessible to people who are not very wealthy results in the public experiencing a disbenefit, because the articulate, influential and powerful parents of children in that system have no vested interest in having a well-maintained state sector."
Mrs Sischy replied: "We do not accept that the definition of public benefit relates only to the state education system; we think of public benefit as something that relates to the whole nation. Most of us are teachers who are trained to teach children and young people, regardless of where they come from, who they are and whether they are poor or wealthy."
The 31,000 youngsters in independent schools came from "hugely diverse backgrounds". But she admitted later that only one in 10 received scholarships or bursaries because their parents could not afford the fees.
In response to John Home Robertson, Labour MSP for East Lothian, Mrs Sischy said it was "very likely" that a child of average ability whose parents could not afford the fees would win a place.
Mr Stoer added: "It is fundamental that no parent who wishes their child to come to our school will be refused on financial grounds alone. We want to have a policy, which has to be limited because resources are limited, of being able to offer a place to any child who would benefit from being at St Aloysius' College - and that benefit is not necessarily academic."
Linda Fabiani, SNP member in central Scotland, pressed home the point and asked "whether some people can pay to be in a private school regardless of their academic ability, while others who apply for financial assistance may have to meet an academic test".
Mrs Sischy told her: "There are probably examples of both."
Mrs Allan argued that there would always be a need for independent schools which provided a niche for youngsters who did not fit into the mainstream.
"In a utopia, the state might be able to provide everything, but at the moment it does not," she said.
Scott Barrie, Labour MSP for Dunfermline West, demanded to know "why it is necessary for the independent sector to have charitable status to achieve those aims, when the state sector seems to be able to do so without that status?"
Mrs Sischy responded: "In our view, all schools should have charitable status."
Christine Grahame, SNP member for the south of Scotland, said she accepted there was a distinction between Donaldson's and the Steiner schools, and schools such as Fettes College. "People are astonished to learn that Fettes, Loretto, Gordonstoun and so on are charities," she said. "People have a clear idea of what charities are for and they do not think that those schools are charities."
Mrs Sischy told her: "As the law stands, such schools are charities because they provide for advancement of education without personal gain or profit.
As they see it, they give back to society more than they receive in terms of public benefit."