However, I do believe we see evidence of approximate logical reasoning in these models, as well as the concept of abstraction.
Furthermore we can take statements generated with statistical techniques and validate them mechanically with older techniques. This is basically what recent work in automated theorem proving using deep learning is about.
Generating logical statements using heuristics and then validating them mechanically also sounds like a reasonable approximation of what a human often does, speaking as a human.
I think I agree with that, but I might add that humans who understand a topic well can also make novel connections and uncover further implications that might seem illogical at first glance. This process of "insight" seems poorly understood by everyone, but I think it goes beyond validating heuristic intuition.
Maybe it makes more sense to talk about predicting the behavior of a system independent of the composition of the system.
I've had the misfortune of working on teams where the hiring manager subscribed to this philosophy.