Actually, the entire premise is illogical. If the Talosians can create such illusions why not just create the illusion for Kirk that they have Special Orders to take Pike to Talos IV, no questions asked?
Probably because Kirk would question it. The Talosians probably felt like they needed to manipulate the situation to provide Kirk a rational explanation that he would accept, and not press the issue too hard.
Or they figured that Kirk would want to beat Spock himself for lying to him.