My understanding of the article you linked is that "moral naturalism" is sometimes used to refer to a kind of moral realism which does not seek to reduce morality to mental properties, but rather holds that moral facts are objective facts grounded in natural reality - the claim of this kind of "moral realism" is not as narrow as you suggest. It is perhaps a compromise between grounding morality in something non-natural, and the position you suggest, which is reducing morality to mental properties. Someone that holds this position could ground morality in something non-mental, say social relationships. It is kind of like saying morality is a natural property of human life as another kind of animal life - there is nothing inherently "spiritual" (i.e. non-natural) about human morality, but neither should morality be reduced to mental properties, since behaviour between animals of the same kind (and for that matter, perhaps, of different kinds) is never simply reducible to their mental states, it is also ingrained in their "natural" social conditions.