The dollar is most certainly backed by military of the Corporate States. This is eminently observable to the rest of the world, who tend to get "regime changed" when the talk comes about not using the USD.
The leaked, then, declassified emails about Gaddafi and how his "Gold Dinar" was considered a threat really opens your eyes on why the Corporate States maintains a very big stick to hit anyone they don't like in the world and most especially nations who were foolish enough to disarm, stupidly trusting the Corporate States.