No. You must tell the truth in the Ancient Language, but if you only
think that it is the truth, but it isn't, you can still say it in the ancient language. So, if you honestly think that something is true, even if it isn't, you can say it in the ancient language. So...Murtagh could have
thought he wouldn't betray Galbatorix, but he finds out that he actually will because of something Galbatorix did.
Go read a different signature.