But that is a specifically crafted scenario and has nothing to do if the system is private or not. I mean at home you have privacy. Just because someone could break into it does not mean its never private. The Linux PC is private out of the box and by default, because no one else has access to it. You just created a scenario that is not out of the box, but compromised or stolen.
I understand the issue you bring up here, but the chosen language you use is wrong in my opinion. That is why the misunderstandings and why people don't agree with your statements. I think you are thinking in terms of "Private mode in a browser".