Obviously, "reading" books they have memorized isn't reading. To me, they have to be looking at an unfamiliar source and reading it to be "reading". Otherwise, it's just memorization.
Children may read books that are familiar to them early on because of the familiar context, which helps them figure out some of the words even if they don't have the book committed completely to memory. Despite all the talk about children having photographic or near-photographic memories, they are actually very rare. I suspect that it would be a rare pre-reading/early-reading child indeed who could recite from memory the complete text of all the child's favorite books without error, or even the hidden text of every page upon seeing the picture of the page. There's bound to be
some reading going on.
