It is true for people who stutter in the same sense that it is true for people who don't stutter. Anxiety, in some people, results in increased muscle activity (rigidity and tension). This can cause motor acts (e.g., speech) to appear uncoordinated. Anxiety, in some people, can also result in increased self-awareness (e.g., behavior monitoring) this results in fewer cognitive resources available for language processing (more interjections and revisions in speech). But it's not anxiety, per se. It's the reaction people have to anxiety (this is an important distinction).