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)
This is one of those situations where it would have been prudent to take the kid home if DUI wasn't the route to take here. We actually have an SOP for this regarding minors. Arrest isn't mandatory but at a minimum I would have lost some pay if I did the same thing. Who hasn't been bit on the a$$ at least once when trying to give someone a break?