There’s another survey--described in this article--that points toward the weakness of our schools as transmitters of anything like our full cultural legacy. Yes, the kids get Martin Luther King, but not Martin Luther; civil rights, but not so much the Civil War.
And this explanation won’t wash: it is, after all, possible to read about our history and culture.
I haven’t yet seen the report itself. When I find it, I’ll provide a link and will doubtless have more to say.