>> Our brains are fallible, and so only approximately equivalent to Turing machines; and even ignoring that can only compute every computable thing given both infinite error-free storage capacity (which they don't have internally or externally) and sufficient time to execute the necessary steps of the computation.

So are actual computers. They're just "less fallible" and closer to a Universal Turing Machine than human brains in certain ways. A Commodore 64 is also incapable, in practice, of computing certain computable functions, due to memory limitations and what have you, but nobody would really claim a Commodore 64 is not Turing complete.