The logic would be correct if, when Yovanni lied, he would always say it was Xavier Williams. In that case, there would be (roughly) 1⁄100 “Yovanni lies and says it was Xavier” for every 1⁄1,000,000 “Yovanni tells the truth and says it was Xavier.”
But if Yovanni lies randomly, and you have no prior that he would lie and say Xavier any more than he would lie and say anyone else, you have 1⁄100 * 1⁄1,000,000 “Yovanni lies and also Yovanni says it was Xavier” for every 99⁄100 * 1⁄1,000,000 “Yovanni tells the truth and says it was Xavier,” which is 99% truth.
The logic would be correct if, when Yovanni lied, he would always say it was Xavier Williams. In that case, there would be (roughly) 1⁄100 “Yovanni lies and says it was Xavier” for every 1⁄1,000,000 “Yovanni tells the truth and says it was Xavier.”
But if Yovanni lies randomly, and you have no prior that he would lie and say Xavier any more than he would lie and say anyone else, you have 1⁄100 * 1⁄1,000,000 “Yovanni lies and also Yovanni says it was Xavier” for every 99⁄100 * 1⁄1,000,000 “Yovanni tells the truth and says it was Xavier,” which is 99% truth.
Right, which is why the claim is immediately more suspect if Xavier is a close friend/relative/etc.