You see, in reality, they belonged to someone else. They belonged to another family. Jesus very clearly represented the Family of God. These people, who were supposed to represent the Family of God, were not representing the Family of God. They were representing someone else.
It means he has nothing to do with it. It does not mean that he will not use it, because Satan will use truth to deceive. And what usually happens in such a case? We get a mixture of truth and error. You know what James says about a mixture of truth and error - it is all bad.
Jesus is implying that these people, too, are liars. Should we go further? Let us go further. It does not end. Let us go to Mark 7.