Is HN a thing that can be abusive? This is a serious question. Don't say yes or no yet.
As far as I understand it: people are abusive. Places, or groups, can only allow for abuse, perhaps systematically, but cannot abuse anyone by themselves. On the other hand, places, or groups, can prevent abuse themselves. (I'll get to that in a moment.)
In this case, specific people choose to act badly toward Mr. Shaw, anonymously. I would think they would continue to do this in a different venue, if their ability to do it on HN were removed. (By stating this, I'm trying to short-circuit all the talk of whether HN is a place that incentivizes or disincentivizes such talk by banning people, etc. In the end, it doesn't seem to matter if such talk is discouraged on HN; the talk will still be generated somewhere else, and will percolate around the internet until it reaches Mr. Shaw all the same.)
On the other hand, HN could help Zed figure out who is anonymously slandering him. HN could put him in touch with these people. They would probably stop after even a plain small-talk conversation, due to having generated even a shred of empathy for the man.
But is this HN's responsibility? Maybe! Right now HN is just barely moderated at all, and even that's a step up from when it was pg's hobby that he had no time for.
HN would be a very different place if it was trying to behave in a "role model" fashion toward the tech community. Maybe you'd have to tie your (long-lived, active) Facebook/LinkedIn profile to your (thus forced-to-be-unique) account, which the mods would then see even though you'd then get a choice of pseudonym. Maybe "throwaway accounts" would only be a temporary privilege granted by asking a mod to make one for you in an exceptional circumstance, and only exist within one post-thread. Etc.
I can certainly see ways in which HN could be systematically less tolerant of abusive behavior—trying to stop it at the source, rather than just making it go somewhere else. But is this a fight YC wants to fight?
I could see this ending with HN being handed over to its own community under some foundation, because YC doesn't want to take responsibility for shepherding the tech community in the way I'm talking about. I could also see YC think that doing exactly what I said above would be a great PR move. What I can't see is HN being shut down: if it was, everyone here would just flock to another place (Lobste.rs?) and continue to be the same community.