The best thing parents can do is to make sure their children to see them reading. Books or magazines, makes little difference. That will instill reading into their identity, and no teacher will be able to dislodge it because reading is not primarily connected with school. Becoming an independent reader also contributes to becoming an independent thinker.
Yes, parents and grandparents need to step up. Mine were giving me Nancy Drew, etc, from age 8, and caught me reading Forever Amber when I was 10. (Locked that one up.) So when my grandson was 10, I was sending him Jack London, H G Wells, Kipling. He became a real reader - and a Marine.