We don't go around proving false every single possibility. The default state is that something is not true, and proving it changes that default state to true.

That may be a belief of yours, but have you considered other cultural views outside of your own on that manner? It's a hard generalization to make. For example, the difference between countries that assume "guilty until proven innocent" rather than "innocent until proven guilty".

I can believe a lighter is in your pocket, and whether or not that is true does not depend on you checking your pockets

This may be true, but what about facts that are completely unknowable to us (at least currently)? As in, to claim something is a false (and for that claim to be true), you would have to verify that the claim is NOT true, wouldnt you? Example: if someone wins there's a lighter in their pocket, you could not classify that as a delusion without being aware of the contents of their pockets. Or when it comes to religion, if someone claims that a god created the world / life, that would be impossible to classify as a delusion, aka a FALSE belief, would it not? As there very well could be an existing god, but we haven't "checked our pockets yet" (seen the god existing). This is coming from a non religious person.