You don't have it quite right. It's that the burden of proof lies with the claimant. The person hearing the extraordinary claim is allowed to dismiss it without proof.
That does not mean that the person hearing the extraordinary claim is forbidden from proving the claim false. No, if they can construct a disproof, that ends it as well.
Russell's teapot is a thought experiment. We have no way of proving whether or not a teapot is orbiting Jupiter. However, we now have the JWST that could watch it for a long enough period to say it never once turned up. But, the point is it is an unfalsifiable claim. Such claims may be dismissed, too.