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.
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“Traditional” social media is not meant to be private, what you post always has been public knowledge, and stays that way.
There are certainly advantages and drawback to this open approach. So use a chat app if you want private social media, like signal story.
While I don’t disagree with what you say, it’s always safe to assume that once something had been online, anybody can copy/screenshot the content.
Things you post publicly online just aren’t private
