I don’t understand why a parent would not jump at the opportunity to converse with their child…
When you see the child reading the paper, ask their opinion, engage them you may be pleasantly surprised of how much they already know and that you as a family are doing a good job. On Shabbos afternoon when you are reading the paper show them other articles and discuss them. Wouldn’t you rather them hear from you what you deem appropriate and honest? How special she will feel when you include her and allow her to hear emes and not the shtuss from her friends on the playground.
All too often we make ossur things that we are fearful of. Maybe if we address it with chachma we will have less children leaving our derech because of their perceived untruths.