By evidence I mean something in some data somewhere that's more than just the opinion being posted, which we can look at and evaluate objectively. I know that's a bit of a lame answer, but I can't give you specific examples without giving the same examples to others who would want to circumvent leaving evidence in that way.

The main thing to understand is that we need something to look at other than just an opinion that one commenter was expressing which another commenter didn't like. That's evidence only of difference-of-opinion, not abuse.

Such data isn't always secret and isn't always just on HN. For example, if someone is asking for HN upvotes on Twitter, we sometimes get links from eagle-eyed HNers. Similarly when someone is sending out spam emails trying to organize a voting ring. And sometimes spammers copy comments from other forums and paste them into HN. Those are pretty basic examples but I hope you can see that in each case there is some objective data that supports a judgment of abuse.

Conversely, suppose you like $BigCo and someone else hates $BigCo, sees your comment praising them, and replies "how much are they paying you, shill?" That's the kind of thing we don't allow, because there's literally nothing supporting that judgment. The same type of commenter will see various comment arguing for $BigCo in HN threads and then post to other threads with high confidence that "HN is overrun with astroturfing". What they mean is that it's overrun with comments they don't like—and even then, "overrun" is an exaggeration.