Yeah it's a bit of both but there's quite some societies which were educated and turned uncivilized or where you have an educated elite that's not really civilized/interested in civilising. Meanwhile pretty much all civilized populations end up educating people,I don't think I've seen a counter example.

It's a lot easier to educate a decent portion of society than create a society that's civilized as a whole. And I think the latter is more important for keeping things running long term which is grim.