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This essay makes a correct appraisal of Less Wrong thinking, but it denominates the position confusingly as "natural rights." The conventional designation is "moral realism," with "natural rights" denoting a specific deonotological view.
A more charitable reading than than provided by commenters would have understood that all the arguments invoked against natural rights (as well as the arguments attributing natural-rights thinking to Less Wrong) hold for other forms of moral realism, in particular utilitarianism/consequentialism. For an argument that utilitarianism is necessarily a form of moral realism (and other problems with utilitarianism) see "Utilitarianism twice fails".
In short, substitute "moral realism" for "natural rights."
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This article would benefit from working through a concrete example.
If you become super-exponentially more skeptical as the mugger invokes super-exponentially higher utilities, how do you react if the mugger tears the sky asunder?
You become less skeptical, but that doesn't affect the issue presented, which concerns only the evidential force of the claim itself.
If someone tears the sky asunder, you will be more inclined to believe the threat. But after a point of increasing threat, increasing it further should decrease your expectation.