Derivative works of course being protected by fair use.

And if Genius is hosting the page that's annotated, that's one thing. If they're simply proxying it on demand and adding annotations, then I don't see how it violates copyright unless every proxy server violates copyright.

Derivative works are what are banned by copyright. They are the things that are not covered by fair use. Transformative works that really change a work aren't covered by copyright because they don't really count as a copy anymore. Fair use is this other thing https://en.wikipedia.org/wiki/Fair_use#U.S._fair_use_factors

The key difference is that proxy servers don't copy content. They reflect it. You can put any URL on the internet behind a proxy server-- that does not mean that the proxy server has already copied the entire internet. Nor does it mean that once a URL has been proxied by a proxy server does the content remain cached or copied-- since in our case at Hypothesis, and we presume at Genius, it does not.

This is a key distinction that separates proxies from caches and archives.

This does more than proxy, the genius proxy alters not just the underlying code that makes the content, it alters the way the content is intended to be consumed.