That would imply that the G factor might have something to do with the gap in achievement though. And if that were the case we'd have very little justification

That would imply that the G factor might have something to do with the gap in achievement though. And if that were the case we'd have very little justification for aiming to improve low income scores. Since we have evidence that students do better as family income increases I'm thinking we are wondering why we can't close the gap called by other things.