There actually is proof, and it's this: there was no review. Never. Not one. Nathan Grayson has never reviewed Depression Quest. Period. Full stop. Stop repeating this easily disprovable lie.
There was positive coverage - and that is how the original reports went - but others who read it assumed that meant "review" when it didn't (and they didn't look into it for themselves).
Worse, many took "being in a relationship with someone you're covering" to mean "trading sex for coverage" which is totally out of line. No one should be accused of such an intention without any kind of evidence, and rarely would there actually be evidence of something like that. Besides, most people who are in some kind of relationship with each other are going to be because they want to be.
I'm sure you already know what that positive coverage was, but it refers to two things. First is the Rock Paper Shotgun article with 50 new Steam greenlight titles, where Depression Quest is featured by: referred to with the sole screenshot, referred to with with a pun ("Acceptance Quest") in the piece title, listed as one of three games especially worth checking out, and given as one of the two games in the tags. Call it blown out of proportion, but I think there's a pretty good case that this is the most prominently featured of the 50 games in that piece. I also personally think that for an indie game plugs are everything, and drawing subtle but heavy exposure to it and giving a single sentence of praise separating it from several other can be at least as impactful as an actual positive review. But that's just my opinion.
The other bit in Kotaku was his coverage of Quinn after she lead a mass withdrawal from the game jam she was in, decidedly showcasing her point of view in the matter.
The thing is, Kotaku EiC Stephen Totillo actually agreed that Grayson shouldn't have written the article if he was romantically involved with Quinn, or else he never would have found reason to ask him (and he said in a series of tweets that a journalist should recuse himself in such a situation). The response was that they only entered a relationship shortly after the game jam article, so there wasn't a conflict of interest. I'm not going to dispute this claim, there's no evidence to the contrary, but if Totillo thought it was a fair question to ask why is everyone else being skewered for showing interest in it? That's not to say Quinn wasn't harassed, but that doesn't mean the whole question was rooted in a fabrication, or that discussion of it should have been grossly censored.
At any rate, deeply ingrained lies are just as rooted in the other side. Here's a popular one, recently uttered by the New Yorker:
"This controversy arose after a jilted gamer wrote an online screed accusing his ex-girlfriend, a game designer, of trading sex for favorable press coverage."
But repeated pretty much verbatim by several publications beforehand. When the reality is, said "jilted" ex Eron Gjoni never wrote in his blog post any claim accusing Zoe Quinn of trading sex for favorable press coverage. So where is everyone denouncing such a blatant lie? I mean, Eron has received plenty of harassment as well, doxxing and so on (including of his parents). The difference is, one side of the lies is coming from disgruntled individuals who largely lack a voice outside of some quarantined forums of the internet, while the other is more or less the mass media. Is it really so off base to question this too?