I would disagree with this on a technicality that changes the conclusion. It's not that human reasoning is statistically predictable (though it may be), it's that all of the writing that has ever described human reasoning on an unimaginable number of topics is statistically summarizable, and therefore having a good auto-complete model does a good job of describing human reasoning that has been previously described at least combinatorially across various sources.
We don't have direct access to anyone else's reasoning. We infer their reasoning by seeing/hearing it described, then we fill in the blanks with our own reasoning-to-description experiences. When we see a model that's great at mimicking descriptions of reasoning, it triggers the same inferences, and we conclude similar reasoning must be going on under the hood. It's like the ELIZA Effect on steroids.
It might be the case that neural networks could theoretically, eventually reproduce the same kind of thinking we experience. But I think it's highly unlikely it'd be a single neural network trained on language, especially given the myriad studies showing the logic and reasoning capabilities of humans that are distinct from language. It'd probably be a large number of separate models trained on different domains that come together. At that point though, there are several domains that would be much more efficiently represented with something other than a neural network model, such as the modeling of physics and mathematics with equations (just because we're able to learn them with neurons in our brains doesn't mean that's the most efficient way to learn or remember them).
While a "sufficiently huge autocomplete model" is impressive and can do many things related to language, I think it's inaccurate to claim they develop reasoning capabilities. I think of transformer-based neural networks as giant compression algorithms. They're super lossy compression algorithms with super high compression ratios, which allows them to take in more information than any other models we've developed. They work well, because they have the unique ability to determine the least relevant information to lose. The auto-complete part is then using the compressed information in the form of the trained model to decompress prompts with astounding capability. We do similar things in our brains, but again, it's not entirely tied to language; that's just one of many tools we use.