I have no prob with the conclusion of that episode, but Kivas is putting a lot of faith in Data's not wanting to destroy any one-of-a-kind artifacts*. (My fanwank as to why the idea isn't even brought up). Data also could have taken Kivas head off by throwing a vase at it.
Edit: I'm watching the ep now. The scene where Geordi is in the Ready Room and saying "It doesn't make sense."....wtf is Riker sitting on? A high chair? His butt is at Picard's face-level. Who sits in a chair two feet higher than every other chair in the room?