So I'm a little confused with the premise of the statement- that by failing to prove that something exists it means it doesn't?
I can't prove the ocean exists, but if you go to the beach and see it, you can either decide it exists, think it's something else, or think you have hallucinated it's existence. In other words, if experience doesn't show something exists to someone who has as a premise that it doesn't, nothing will prove it because his premise is already set, and nothing will convince him it does.
That's why in logic, you cannot prove a negative.