Agreed, though it's not so much about "owing" them the truth as it is to prove their instinct to trust you right, not wrong. A much stronger foundation for your future parental relationship.

The only real question should be then whether you ask her not to tell other kids.

"Some people like to believe that such stories are real. Believing the story makes them happy, like when you pretend-play you're Darth Vader in Star Wars. They may become sad, or even mad at you, if you tell them the truth. That's why when you hear someone say something wrong, you don't have to correct him/her right away. However, if you are asked for your opinion, you can tell them the truth. If people become angry at you because you answered truthfully, you tell daddy, and he's gonna beat them with a stick, ahem, and he's gonna talk to them."

Don't like to children.

Freud would have loved that.