I think the article dances around what people really mean when they say "you can't prove a negative". The writer touches on it but somehow skirts the real issue. When we say "you can't prove a negative" you're really saying that in order to prove a statement of the form "not exists x P(x)", it's equivalent to proving "for all x not P(x)" and so you're really making a statement about EVERYTHING that has or does or could ever exist somehow. These proofs are either analytic and trivial (i.e. there doesn't exist a rectangular circle) or not proofs.

He suggests you get around this by providing an argument about unicorns and then goes on to talk about how premises don't always need to be justified, but the problem is proving the nonexistence of a thing -- and he provides a formal deductive example of a proof of nonexistence of a thing by instead substituting as a premise nonexistence of another thing (evidence). Sure, if you can prove no evidence for unicorns exists and that for unicorns to exist they MUST have left evidence you can prove they don't exist. But the first one is a reduction to the original problem -- in order to show something doesn't exist (be it unicorns or evidence for unicorns) you need complete and total knowledge about existence, which no human up to this point has had enough hubris to claim, and the second requires a level of certainty that doesn't really exist.

If we're discussing the existence of a thing that doesn't leave evidence (god) especially it's very fair to say you can't prove a negative and I think his attack on this tactic is a non-starter.

There has never been even the tiniest bit of evidence against the existence of god. There is certainly evidence against a god with specific qualities; a benevolent god, a god that wants this to happen, etc. But if you don't require god to have any specific qualities there isn't a shred.