Exactly - it's too easy to say that Twitter is simply a reflection of society itself, technology is not a completely neutral pass-through filter.
The 140-character limit strips all nuance out of conversation, so it's no surprise that when it comes to controversial topics everyone is an asshole. It turns out we need more than 140 chars when talking about complicated, important topics.
More than that, Twitter's choice of how users relate to each other also contributes to the nastiness - it's a medium specifically designed so that a single message can traverse a huge portion of the user graph, and this causes a lot of problems.
On Facebook, if you post something stupid, insensitive, or generally moronic, at worst you'd have your friends (or friends-of-friends) telling you off, it almost never goes beyond that simply by nature of how friending works. FB's privacy settings (by default at least) literally prevents anything from being shared past N distance from you.
Ditto on old-school web forums - if you post something stupid, insensitive, or generally moronic, you'll at worst be dogpiled by the forum's own users, but that's it. The link may be spread around, but few people will sign up to some new phpBB webforum just to yell at your stupidity.
On Twitter though your tweet goes viral and traverses many, many different communities, each of which get to layer their own outrage on. More than that, they are all free to respond to you, without filters. The pile-on effect is the scariest we've seen from any social network in existence.
Reddit also suffers from a similar problem - communities cross into each other almost too easily, so brigades are common. At the very least though most subreddits are moderated, whereas Twitter is really a free for all. We've seen how well Twitter's abuse team handles overt death threats and other far-beyond-the-pale abuse (read: lol).
This might not be particularly insightful coming from someone who never really got into Twitter, but their whole model of user interaction is fundamentally defective.