The issue here is burden of proof, and the fact remains that it is impossible to prove at least some negatives.

Proving that there are planful medium-sized organisms with big brains is easy, but proving that they are unique in their planfulness is impossible. The tilde argument isn't so much that the negation has no positive version (every proposition has a contrapositive that is equally true), but that the burden of proof must fall on the one claiming a falsification. Theist's say something exists that falsifies atheism. Atheists do not claim that anything falsifies theism. The burden of proof must be on the theists for that reason.

I think the arguments about nephews, etc., are not on point. Let us put the burden of proof on the person who says that there are nephews. That person adduces an uncle and wins the day. ("Why ask if shad do it? Waiter, bring me shad roe!") The burden of proof is on the person claiming fish do it; he just happens to have to goods. Can theists make the same claim?

Perhaps Occam's razor is another way of saying that the burden of proof is on the one who would introduce a falsifying entity. In other words, the score is not so much 1 to 0 as it is n+1 to n.