The HMC definition of public school seems to have drifted considerably as far from the common usage (as evidenced by the numerous reference I have provided above) and the HMC website doesn't even use the term 'public school' on its home page, describing its scope as "HMC (the Headmasters' and Headmistresses' Conference) represents the Heads of many of the world’s leading independent schools". Indeed the HMC website only make one reference to the term public school on a page where it is quoting from The Times.