I have no idea how much efficiency this buys them, but the same mechanism can be used against a blacklist of known copyright or illegal materials. In this case, having a hash that matches something in the copyrighted materials list AND sharing it triggers this action.
Just as easily, putting some child porn in your DB could also have them check against illegal material hashes and trigger an automated notice to some law enforcement agency or something similar.
This can even be used for National Security without violating the classified contents of the documents. Say another Snowden-type grabs a bunch of classified documents. The agency could give DB a list of hashes with instructions to "call us" if a user uploads a bunch of leaked documents to their DB. They could even do this blind, just send DB a hash of every classified document or piece of data they ever produce and catch leakers before anybody in the agency even knew something was leaked internally.