I agree and disagree.  Stutterers stutter for reasons they normally do AND they stutter for reasons normal people do. Stuttering caused by the anxiety of stuttering is not caused by stuttering directly.  In that sense anxiety can make a stutterer stutter more than they normally would and thus these instances are caused by anxiety directly.  Example: taking beta blockers can help reduce stuttering (helps remove anxiety-based stutter) but won’t completely remove it (since it isn’t the root cause as you say).