Is the answer wrong??
you use H+ and OH- when it is given that the reaction is carried out in acidic or basic medium.Nothing is given so we have to consider it being carried out in neutral medium.Apply the ion-electron balancing for neutral medium method.Waise there's no need of thinking about the medium.This reaction is a simple inter-molecular redox and so it is balanced before you reach that step of adding H+ or OH-.And why are you even bothering about knowing the oxidation state of I in I3- ;that is required if you are applying the oxidation number method of balancing.