The Scottish Charity Regulator said that in its evaluation, St George's School for Girls, Fettes College and St Columba's School had failed to pass the test.
They include the party's new leader, David Cameron, who also went to Oxford University - as did Labour leader Tony Blair following his schooling at the private Fettes College.
His father was a well-to-do builder and architect who, when the family moved to Scotland, sent his son to Fettes College, the so-called Eton of Scotland which Tony Blair was later to attend.