They said that in the first couple of pages. I know it's long and wordy, but it gets more practical and down to earth the further into it you go. They have addressed your concern in quite a lot of detail.
My point is that they kind of dismiss previous approaches using this only logical argument, which is not applicable anyway. Using such a rigorous logical reasoning in the realm of social science demonstrate either a misunderstanding of logic or a purpose to mislead the reader.
While I am simptethic to the notion that social "POLICY" should not be set by logical arguments alone. Social "SCIENCE" is another animal and logic and sound science is the only way to understand reality. How can we hope to design effective social policy if we refuse to try and understand reality? What are we misunderstanding about logic? I find your comment about misleading the reader especially ironic.
I agree that whole argument seemed quite artificial. I took it as a way to complain about other researchers who apparently had assumed that all stereotypes are somehow false, whatever false means. I'm sure they didn't mean it must hold for each individual in the group to be accurate.
But the definition that they use is "a stereotype is a set of beliefs about the personal attributes of a social group." How can that be interpreted as anything but something that holds true for each individual of a group?