I remember being at a party where two people got into an argument about abortion. It was exactly what you would imagine, a completely pointless exchange of rehashed ideas that the 10 people watching the conversation have heard a million times.
Then someone chimed in - not to argue but just to drop a fact they possessed that nobody else in the room knew. It didn't change the arguers' minds but it took the other ten people aback like "how come we heard this debate a 1000 times but this very important fact never gets mentioned?"
So that random quip influenced 10 people on a very polarizing issue. That's powerful.