Lots of people do that. I identify the university I work at in my twitter profile. Obviously I do not tweet on behalf of my university; it's just a way of describing what I do in my day job. Sometimes I tweet negative things about people. It's just words; you know, people talking to other people. Sometimes they even do it in public, like we're doing right here.

It's not obvious who you represent when you have list an employer in your title or bio. The point of listing it is that you're adding that affiliation and connection. Worse are not "just words". If that were true, libel wouldn't exist. Libel can cause significant damage and the connection between your twitter account and your employer makes them a target. So you might want to ask the University's legal department before you assume that they're ok with being connected to you on twitter.

Yes, I recognize there are some narrow exceptions such as libel, and I'm perfectly fine being held accountable for libel. If I post something which actually libels someone, i.e. something which a court will hold me accountable for having posted, then that's fair, and I'll take full responsibility.

What seems to be in question here, however, is whether people may post truthful comments on twitter, which under U.S. law are by definition not libelous.

It's more than just libel though. While truthful, your employer might not like being associated with the opinions that you're sharing. That's why employers have social media policies - to protect themselves by educating their employees so that they understand that the employee can be held accountable for the opinions shared via social media if that employee is identifying themselves online as being associated with that company. It is extremely common, and I would suspect your University does have an opinion on the matter - especially if it's a State funded school. Then especially, you're a State employee and are representing that larger group too.

are you seriously arguing that if you mention your place of employment on your personal website or blog, they then have the right to police everything you post there?!

Nope. What I'm saying is that once you do that, you run a much higher risk of alienating your employer by saying or doing controversial things. They certainly can't control what you do or say, but they may well opt not to employ you because of the choices you make. There's a distinction there, and it matters.

(Also, in this case, I do believe that she used her twitter feed for 'official'/work-related duties, so that does genuinely blur the line between personal and professional)