Here's how a defender of the Principle would answer that:
You would not be able to show up at the War department on December 5th, or at any time before the actual attack. Nature would prohibit it, just as nature prohibits a person from jumping 50 feet into the air.
Perhaps your car would brake down on the way. Or perhaps you would fall into a coma on December 4th, and not wake up until December 8th.
I'm not saying I agree with any of this. But that's what a defender of the Principle would say.
If someone went back and changed the past, we’d never know, because we’d be in the subsequent new future.
LeGuin touched on this in Lathe of Heaven. There would be no way to know, since to us, history is what did happen.
The principle is unprovable.