Dame Judith Mayhew Jonas was speaking at the Public Administration Select Committee hearing on education and public benefit on 2 July.
"Most of our schools are carrying out far more than the bare education of children," she said. "They are good participants in the broader community."
However, she admitted that the council had no hard evidence, and that her assertion was based on "instinct".
She denied the public benefit test had caused consternation in the independent sector, and said the media had "whipped up a frenzy".
However, she said the Charity Commission's draft guidance on public benefit and education went beyond the powers given to it in the Charities Act 2006. She said: "The commission is a regulator, not a policy formulator."
Anthony Seldon, headteacher of Wellington College, said the suggestion in the media that private schools were only now scrambling to do good work in order to pass the public benefit test was "demeaning" to schools.
He said the commission should not focus on assisted places as a means of demonstrating public benefit because they deprived the state system of its best pupils and were abused by middle class parents.
Simon Jenkins, a columnist at The Guardian, said he had been a governor at two private schools, but had never heard the board discuss its charitable role. "We were just desperate to move up the league tables," he said. He described the commission's draft guidance as "a reasonable request for a prominent part of the charity sector to justify itself".
Tony Wright, chair of the committee, asked why private charitable schools weren't queuing up to take on hard-to-teach pupils to fulfil their charitable ethos. He said: "This would demonstrate the things the private sector claims for itself – if it succeeded where the state sector has failed."