Any numerical system operates only on numerical, not logical/grammatical/whatever constraints. Wrongness is built into any system based solely on neural components by the simple fact that rightness is unverifiable from within these systems' own "logical" (read: associational) apparati.
I share your confusion regarding the grave dearth of incredulity in the reception of these technologies.
I guess you can say the human brain operates only on the data it gets from our ear drums, optic nerve, etc. Might as well call that numerical input, it’s certainly not grammatical or logical, all that is internal and arises after many layers of neurons.
I agree: the human (or any organic) brain is no more "logical" than any other numerical system. We obscure this fact (mostly) successfully by virtue of the statistical regularities with which we are imprinted as a result of our experiences. This gives the appearance of logical rigor, but this rigor is only illusory.
I share your confusion regarding the grave dearth of incredulity in the reception of these technologies.