Yes, because humans have a reference to the world and they can, in some cases check the claim. The examples you give are not facts we can directly check, we take it on authority that they are true or not based on individual conceptions about the validity of the authority. Even the cases you mention provide another example of what this "AI" cannot do: it cannot dispute facts, because "the world" is not in it's domain of reference. It's domain of reference is text previously produced by humans and all it can do it manipulate that to produce something hopefully useful to us. Even there it is not very good, otherwise it would be producing new mathematical theorems, since you don't need a reference to the world for that, but it doesn't "understand" logic well enough (if you can say it understands anything) and it doesn't have the concepts to do it.
Sure there is and it's a basic one: can it determine a fact?