The best defence of this question would be to say that if Pinnochio is lying, then his statements must be testably false.
Put another way, in order to lie, you have to contradict something you know to be true. If Pinnochio has no hats, then he has no facts about his hat collection to misrepresent. So (A) is true because if it were false, he would not be lying, even though he also wouldn’t be telling the truth.
But yeah, posing this as a right-vs-wrong question hinges on the assumption that you will interpret it in an orthodox way. I feel like it rewards the homeworkly kind of intelligence over the kind that takes things apart from first principles.
