In a journalistic context, a ZKP can’t prove veracity of the information.
Let’s say you have a hoax that you want to pull on a journo. You cook up something that looks legit, like the blueprints for a super secret stealth fighter or something. You find a way to apply a ZKP to that file (let’s say an elaborate cryptographic hash). You leak the file to the journo. They ask for you to iterate on the ZKP a few hundred thousand times (which is on the low side for a ZKP) - easy to do, because you came up with it.
But that doesn’t mean the file’s legit. That’s a separate problem, and not one that is technological in nature.