In the US: Fair use disregards licenses. Fair use can be found to apply, or found not apply, by a court of law. Archival of information is generally felt to be Fair use, as is Search indexing.
The real argument is when is AI re-use of copyrighted material a violation of copyright. That is a large grey area that will probably be determined in favor of large corporations and not in favor of individuals. (As in, Disney can use AI writers to copy you, but you won't be allowed to copy Disney)