>If you post public-domain material to your site, you don't "own, or otherwise control all the rights" to it.
I think you'll find that you do.
You own that copy that you are presenting for distribution, no one else owns it nor has rights over it, you do (at least in copyright terms, PD could still have trademark and other issues).
The right to prevent other people copying it is exhausted, there is no [copy]right there to own so it's not a legal right that you don't have. That other people own other copies and have control of all the available rights to their copies is immaterial.
That said I think you're clutching at straws classified documents are not in the public domain unless they have been published by someone with the right to do so and the copyright term in the relevant jurisdiction has expired.
There are about 30 states IIRC that aren't signatories to Berne Convention or relevant parts of TRIPS, etc..
I think you'll find that you do.
You own that copy that you are presenting for distribution, no one else owns it nor has rights over it, you do (at least in copyright terms, PD could still have trademark and other issues).
The right to prevent other people copying it is exhausted, there is no [copy]right there to own so it's not a legal right that you don't have. That other people own other copies and have control of all the available rights to their copies is immaterial.
That said I think you're clutching at straws classified documents are not in the public domain unless they have been published by someone with the right to do so and the copyright term in the relevant jurisdiction has expired.
There are about 30 states IIRC that aren't signatories to Berne Convention or relevant parts of TRIPS, etc..