What. You start talking about "strawman" while building a strawman to knock down. Did "pseudoskeptics" bite you or something?
It's not "negation of claim", it's "negative claim", or claim of absence that is hard/impossible to prove.
For example:
You claim to exist. The negation of that is that you don't exist therefore you are making an extraordinary claim and I am not. So prove to me you exist...
Easily proven, I can come over to your house and knock you on the head.
Now to prove that I _don't_ exist you'd have to visit every single person on the Earth and ensure that he is not me -and you still won't get definite proof, because some people are hiding or missing. Most importanly, I'm actually right behind your shoulder all this time and quickly walk when you turn around.
Of course there are negative claims that are easy to prove, like "there are no million dollar bills in my pocket", but those have a) small enough search space, and b) specific test for positives.
Claims of some specific property in _some_ humans are not provable as negatives in general case just due to sheer number of humans on this planet, but easily provable as positives - just show at least one human with that property. That's what Randi does, looks for positive proof.