Seems like the actual issue was that the law in question would let him be convicted even if he wasn't doing these things and just being a nuisance. It's not that he's innocent, it's that the law used is itself illegal.

To be clear, I do not agree with the ruling, but the ruling was on whether this was a federal or a civil matter. I think the government should strongly prevent clear harassment and reasonable threats of violence, but the supreme court decided that threats or words are not enough in this case. I think it's particularly two-faced, especially in light of threats of violence being used regularly to prosecute minorities and identify potential terrorists, but threats of violence directed towards a single person in the context of years of harassing behavior and a known pattern of behavior were apparently not enough.

If I had to guess, the court was wary of allowing any potential attacks to the 1st amendment, as they have been want to do in the past - a famous example of this in (somewhat) recent history is when the supreme court held that the 1st amendment was more important than the stolen valor act passed just a few years earlier. The ruling doesn't particularly surprise me, nor does Kagan swapping sides because in the US we have a strong free speech identity and free speech limitations in terms of harassment has almost never been ruled on (one might make the argument that virginia v. black might be one such case, but that's a case of racially motivated hate speech which is not quite analogous here).