Why do you think you can’t prove Gengis Khan existed?
Claims need proof when there is a call to action. It doesn’t matter to me if you’re from an island or a small town or a big city, unless you’re giving me directions. If you make an extraordinary claim, and you want me to believe you, then I’ll need proof. If you make a mundane claim, then what the fuck do I care if you’re lying? If you claim to have a disease, I’m going to believe you because I’m not a doctor and it costs me nothing to take you at your word.
If you shout “Run, something bad is coming!” I might feel foolish and angry if I later learn you were lying, but I’d rather be foolish and angry than injured or dead. Proof is a luxury when time is of the essence, doubly so when safety is at risk.
There might be some specific nuances to quibnle over, but generally I think we could reach consensus on the guidelines I described.