I think you should point out what "public school" means in Britain, otherwise there is a 100% chance that any Americans who aren't aware of that definition will

I think you should point out what "public school" means in Britain, otherwise there is a 100% chance that any Americans who aren't aware of that definition will misunderstand your comment. (In the US, the term "public school" means what you mean by "state school", afaict).