[glenra]

That is a popular story, but I'm pretty sure it's not true. Do you have a source?

I suspect you're thinking of the sort of elite academy type schools that have tough entrance exams - but those are a very tiny fraction of private schools. There also exist private schools that that take anyone who applies and even private schools that specialize in special-needs students.

Also: in several parts of the US (including all of Florida, Ohio, Georgia and Utah as well as various municipal districts), special-needs students actually have their own separate voucher system which parents can use to attend private schools because the public schools aren't good at educating those kids.