I mostly agree, but I see two points that might be problematic:
replya) The brain might have an entropy source (then it can't be modeled as a function). Trivially to fix, and in some sense, with diffusion models starting from random numbers, AI has done so.
b) The hidden function might be not computable. I would have no idea how that would work, but I think this is what it boils down to if people say "the human brain is more than a machine".
a) enthropy can be injected as well. In fact there are hidden sources in current training.
replyb) well, it can be the case that, say, certain kinds of computation are either too inefficient or outright impossible within the current model.
Who knows...