Making something available on the internet means giving permission to download it.

No permission is given to download it. In particular, no permission is given to copy it.

Fair use is a defense against copyright infringement under US law

Yes, but it's often unclear what constitutes fair use.

Using the web is rarely fair use because there is no copyright infringement

What are you even talking about.

When training data is regurgitated, that is mostly fair use

You have no idea what fair use is, just admit it.