That isn't the only experience I have had of private school people and I know a lot of people who have similar experiences. And yes I have also noted the fact that some state school people voice concerns and relax a bit more around you if they know you are state school. But I think you are putting the blame a tad too heavily on one side.
And, yes you probably do have more experience, but your evidence is equally anecdotal, and I don't expect I will be the only person contributing to this thread. It is a debate comprising different evidence from numerous people, and I have no doubt a large number of other people will also have had experiences of private school people behaving in a similar way. And just because there are no posts, does not mean there are no private school people with that as a concern, especially if they are going to St Johns.