Bones tells Dumbledore that she has information from four hours in the future and asks whether he'd like to know it. That there is relevant information from four hours in the future is information from the future - she would not have said that if it were otherwise, so it seems there must be exemptions of that kind.

That's information to a careful logical thinker. There's a lot of evidence that magic to a large extent acts as a naive person might expect reality to act. Broomsticks and the bag of holding are both examples of this.