According to google, 87% of Americans go to a state-funded school, so yes judging an American based on the fact that they could afford to be in the top 13% and go to a public school instead is legitimate. This doesn't seem to match what you're trying to say.
You’re using the British definition of “public school” here, which is a “private school” in the US. US public schools are equivalent to UK state schools, in that both are run by the state.
