It is different from a human brain in that it is not a human brain. It is a statistical function that produces some optimized outputs for some inputs.
I have made no mention of things being authorized in public. In the US you are allowed to take a photo of anything you want in public. These models are not being trained on datasets collected wholly in public though, it is very insidious to suggest that they are.
The internet is not "the public". It is a series of digital properties that define terms for interacting with them. Now, a lot of material is publicly accessible online, but that does not mean that it is not still governed by copyright. For example, my code on Github is publicly accessible, but that doesn't mean you can disregard the license.
If you use this copyrighted material to produce a product for commercial gain you will likely face a fair use test in court. If you use it for a non-commercial cause with public benefit you could probably pass that fair use test. Open source will do very well because of this.
The model is not a human though, and very often these are not "public" works that it is trained on.