I get accused of being a liar a LOT. Some times it is because another part was out and I didn't know it, Some times my parts will lie because they don't want the other person to know it wasn't "me" or because they don't want the other person to tell me. Sometimes my mind seems to make up stories to fill in the gaps... it is really embarrassing to have gaps.... I can say though that it has been very rare that any of my parts would lie with malitious intent or to intentionally lie to someone outside our body... It is always ignorance, embarrassment or internal politics. I don't know if that is true for all DIDers but it is my experience.
BTW the safer and more accepted all of me feels (usually more by me than outsiders) the less likely it is to happen. God that is a confusing sentence!!!