I guess I should be happy if this is true, considering my kids go to a public school, but there are just so many unstated assumptions to make the argument work

I guess I should be happy if this is true, considering my kids go to a public school, but there are just so many unstated assumptions to make the argument work that I could almost imagine it saying "...and for simplicity, we assume that students are spherical objects in a vacuum." E.g., colleges know which public/private school each student is from. It's not a blind selection process.