For example, I don't believe in magical mole men who live at the center of the earth and feed on human children; but that doesn't mean I have to prove they don't exist. But, if someone were to claim they saw magical mole men, and started to tell the press, then they would be expected to provide proof of their claim.
All in all, I guess it's a funny analogy, but pointless.
And the second one just wasn't funny. =\