Just because something is publicly accessible doesn't mean you can use it for free, or that it gives you rights to do whatever you want with it.
I can access a public park, but that doesn't necessarily give me the right to also bike on its sidewalks, or walk on the grass, or take some of the plants home with me.
> ... or has been obtained illegally
Similarly, content that is _accessible_ publicly may be illegal to _obtain_, these aren't mutually exclusive.
On the internet, you'll find there are terms of services and licenses. These restrict how you can use even publicly accessible material. Public availability doesn't give you a license to use it however you want.
> Public availability doesn't give you a license to use it however you want.
Of course. You listed complex examples from the real world. A park where walking is allowed but damaging the plants is not, for instance. There it makes sense to distinguish various activities that can be done in there and treat them separately.
But a website offers not much activities that you can do with it. You can read it. And that is about it.