Under the DMCA, you can claim copyright over damn near anything and force a provider to take it down. If there is any ambiguity as to whether you are the owner of the allegedly copyrighted material, like for example legitimate fair use, they still are required to take it down—unless the alleged violator files a DMCA counterclaim in which they must supply their legal name and address to the original claimant. This has been used to silence, or deanonymize, people who post unpleasant things about a powerful person or organization.