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.