If she was indeed officially "warned" it is almost every single department in the conus's policy to issue a warning ticket. Every stop, regardless of how small, that a LEO calls in a plate number, 29/29 wants and warrants is run, a minimum of a field interview with license data etc is recorded.
Do they have that on record ?
There should be something documenting the stop and disposition, even if only a log entry. Always a bad idea to have someone drive off in a questionable state. I was taught if ya wanna give someone a break, then get them a ride home or make sure they can't find their keys (known a couple officers who would throw the keys in the ditch - not my style but it worked).
I presume that, if the officer had decided to arrest the driver, and she put up any kind of a fight and got hurt, then the parents would have been completely understanding, thankful and supporting. And there certainly would have been no talk at all of "false arrest." (OK, sarcasm off)