It would be better to say that someone or some group bears the burden of proof to support any statement. But for the beliefs we take for granted, in our time and place in history, that burden is often deferred.

You personally don't bear the burden to prove that Zeus doesn't exist, since that burden was met by thousands of modern scientists and philosophers who've changed the default assumptions of Western civilizations. You'd defer to the Scientific Revolution instead of having to reinvent the wheel.