I should think that a term such as "annoy" probably has different significance when used in a law than when simple individuals such as ourselves use it. It may sound like an unlimited possibility to us, but perhaps to the legal world it could not be as unlimited.
How on earth can you prohibit someone from being anonymous on the internet? How can you verify it? Is this a case of "if caught doing it, youre in big trouble"? In any case I think its good to have some kind of legal frame to this, so that people cant run wild harassing others. I have had a taste of that and it is really, really distressing.