I wonder if what this really means isn't that it is possible for a culture not to have a concept of amorality. What I mean by this is the following: they have a concept of what things ought to be like, and it encompasses both moral and non-moral imperatives. What they did not realise is that you can just ignore a subclass of these oughts (namely, the moral ones) without rationality compelling you to do otherwise and thereby be an amoralist.
Well Plato argues that "if you know the right you will always do the right". Heck, this idea, in the form that "all problems are caused by ignorance", is still around today.
I was stunned to read the accounts quoted below. They're claiming that the notion of morality - in the sense of there being a special category of things that you should or should not do for the sake of the things themselves being inherently right or wrong - might not only be a recent invention, but also an incoherent one. Even when I had read debates about e.g. moral realism, I had always understood even the moral irrealists as acknowledging that there are genuine moral attitudes that are fundamentally ingrained in people. But I hadn't ran into a position claiming that it was actually possible for whole cultures to simply not have a concept of morality in the first place.
I'm amazed that I haven't heard these claims discussed more. If they're accurate, then they seem to me to provide a strong argument for both deontology and consequentialism - at least as they're usually understood here - to be not even wrong. Just rationalizations of concepts that got their origin from Judeo-Christian laws and which people held onto because they didn't know of any other way of thinking.