The burden of proof does fall upon the claimant. That's why it's so easy to be a skeptic There's no work involved.
I have an aging relative that recalls when he was a little boy there was a cow in his father's herd that wouldn't milk. He followed the cow all day long and eventually discovered that it was being milked by black snakes.
None of the anatomical features of a snake that make this impossible phase him. He swears this is what he saw.
The nature of this type of claim precludes disconfirmation. Proving a negative is a logical fallacy.