Yes and no.

let’s say I have a website that hosts user generated content like a forum or something. Some other person just hosts a mirror of my website that is not under my control. If some user requests me to delete his data, I can do that. i cannot delete the data from the mirror site.

Nothing else is happening in the fediverse. The only difference is, that in the fediverse the license and technology is set up to encourage mirroring content.