"AirTag Detected Near You" popup (do not own Airtags!)

I understand your concerns. The fact is that Apple has tried to make this as easy as possible to understand and how to help people maintain their privacy. It is also to prevent people from using the AirTag nefariously to track people without their knowledge. You can use that information from this support document, What to do if you find an AirTag or get an alert that an AirTag is with you - Apple Support to try and explain to your mother.

If you wish to let Apple know your feelings about this, you can use this feedback link, Product Feedback - Apple They will not personally respond, but they review all of the feedback.

You may wish to check again to see if they are coming up. If not, then you can check the car, but that is how it is supposed to work if there is an AirTag with her that is not hers. But if she is near one, like maybe at the grocery store, that would pop up. That may have been what it was, just long enough for it to show, since it appears from the map there was not a full route. If there are no more pop ups, then I would say that she was probably close enough to someone in the grocery store long enough for it to show it was near her.

Does your mother use public transportation, or has she travelled with someone that may have had an AirTag? That could be what it is.