Agreed. To slightly nuance your last three paragraphs, if the brain exceeded the physical, and if this meant we could do something a computer cannot be made to do, then to prove AGI impossible "all" the proponents of such claims would need to do would be to prove that human brains can do a calculation that is not Turing computable.

Anything else short of disproving the Church-Turing thesis will come up short.

They could start by proving that computable functions outside the Turing computable is possible, because if they are not, their claims would fall apart.

But neither this paper, nor his previous paper, even mentions the Church-Turing thesis.