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The model does not produce statistically indistinguishable from human outputs, but the outputs that satisfy its training rewards system most strongly. Those are very different things. And the rest of the argument is less logically.

How would a machine capable of detecting that difference be usable to train a 'better' model? Only _if_ the goal was to make it indistinguishable from human, which it is not, the goal is to make it succeed at a set of training tasks! Tasks that in fact don't lead to it being all that human like.

And if we assume that was possible, and that such a detector could be used to train better models, which in turn would lead to better detectors, that would not break any laws of information theory of thermodynamics either! That would still require immersive amounts of compute!