B.O.
It is not true lying, it is storytelling. At this age children are still grasping/learning the concepts of reality, imagination, and fantasy, and where the lines may divide or connect. I would not suggest punishment for this, but simply to understand that this is a normal healthy part of child development, and to simply correct the child with the truth. It is not necessary to get the child to "own up". She might not be ready for the concept of accountability yet. The teacher should know this as well, it is a pity she does not. May be you could educate her. I am an Early Childhood Education major, and I learned this in school.