In reality, what you’re saying makes no sense.

Making something available on the internet means giving permission to download it. Exceptions may be if it happens accidentally or if the uploader does not have the necessary permissions. If users had to make sure that everything was correct, they’d basically have to get a written permission via the post before visiting any page.

Fair use is a defense against copyright infringement under US law. Using the web is rarely fair use because there is no copyright infringement. When training data is regurgitated, that is mostly fair use. If the data is public domain/out of copyright, then it is not.