Here “public school” has its British meaning (Eton, Harrow, Rugby School, etc): see http://en.wikipedia.org/wiki/Public_school_(UK).
I have heard occasional old accounts of pupils at the big fee-paying schools called public schools, being ordered to use only Latin, not English, for general conversation among each other, all the time, or on some days, or suchlike. Is this an urban legend, or true? When and where did it happen?