This is a service for publishing your thoughts, your links, etc.; of course it's not private. If you put something out in the public view, anyone can copy it. That's not a fact about the Fediverse; it's a fact about what it means to publish something.
The same is true if you print your thoughts on paper and distribute them as flyers in your local town square. Anyone can grab one and keep it; later on, they can tell people what it says. That is not a privacy failure; it's a publicity success.