This analogy does not make sense to me. We do not have equivalence between all of the infinite inputs and outputs here, we have equivalence in a finite number of cases and known cases where the two functions (human output and llm output) diverge drastically. Any mathematician worth their salt would tell you these functions are definitely not equal.

Now you could make the argument that these functions are close enough most of the time so it won't matter but unless you want to get really rigorous that's more of a stats / engineering perceptive not mathematics. Any more importantly that's very up for debate, especially in a high pressure situation like medicine.

Of course these models are wild and I'm quite impressed with them. I still can be worried about the damage someone who doesn't think things through could cause by assuming GPT-4 has human or super human level intelligence in a niche, high impact field.