This argument is, however, nonsense. The human capacity for abstract reasoning over mathematical models is in principle a fully general intelligent behaviour

While it's true that humans are Turing complete, there does not exist only computability as a barrier to understanding.
Brains are, compared to some computers, quite slow and imperfect at storage. Let's say that the output of a super-intelligence would require to be understood, in human terms, the effort of a thousand-years-long computation written with the aid of a billion sheets of paper. While it would not be, in principle, unintelligible, it doesn't matter because nobody will ever understand it.
You can combine, if you want a more principled approach, Chaitin's theorem and Blum's speed-up theorem to show that, whatever complexity is intelligible for a human being, there's always a better machine whose output is, for that human, totally random.

My suspect is that you are making the same mistake you are accusing LWers: by reasoning by analogy, you see errors in what really are missing steps in your understanding.
What an irony.