It's proven AFAIK. Check out Judea Pearl's (Turing award winner, pioneer in the fields of AI and causal inference) take on the topic here.

As a fellow ML researcher (mostly theoretical) I completely agree with you. The field of AI is still far away from AGI, and I highly doubt neural networks will lead to AGI. For instance, they can't do causal/counterfactual reasoning; they basically are just fancy curve fitting models. Of course this doesn't mean that the latest developments aren't impressive.

I'm not surprised the public has a completely wrong idea of current AI developments, as even "experts" get a lot of things wrong.