In polite debate, the person making an assertion carries the burden of proof - after all, no debate can begin unless the person provides ground for debate. Without evidence provided, an assertion can generally be rejected out of hand.
In some forums, the burden of proof is reversed, and an assertion is allowed to stand unless disproof is offered. Complaints against this sort of thing in jurisprudence led to the American standard of "[[innocent until proven guilty]]
See [[standard of proof]].