But AI companies don’t publicly redistribute the content they scrape, whereas Internet Archive does.

Even if you believe what the AI companies are doing is or should be a copyright violation, the Internet Archive is redistributing in a more direct manner.

Fair point. Being small and shadowy is a sufficient condition to avoid litigation, but not a necessary one. Another sufficient condition is having billions of dollars to throw around. Unfortunately, archive.org is well known, well loved, and fundamentally harmless.

Side note: You probably mean "flout" instead of "flaunt."