You can tell them you think they're delusional, or make it slightly less personal and say what they've said is delusional (linguistically incorrect but a compromise). I mean, it really isn't your responsibility to coddle their emotional state by staying silent. Anyway, I've done both, in public, and the result is interesting. I felt slightly guilty because the person will take great offense even though usually they don't get riled up about it. But at the same time it was less uncomfortable than listening to unopposed lies.

Diplomacy provides for ample indirection: I'm so sorry to inform you so directly, I mean no offense, but what you're saying is completely unprovable, you have no facts at all that can demonstrate your position. I do appreciate your bravery for being willing to expose your ignorance on this topic so publicly, however.

Et cetera.