I've seen cases in which the schools dislike zero tolerance on anything, and not being able to play with the rules, and use a case like this to reduce the policy to ridicule.
The other point is that these kids are minors, and nobody should be giving them a pharmaceutical, over the counter or not. Most schools have a policy that they should be left in the nurses office with instructions. If there's not a policy like that, how are you going to stop the kids from sharing their medications, or having something illegal in an Advil (or whatever) bottle? (And yes, that happens)
Actually, if a student isn't feeling well, like with this girl and headaches, it's probably best to check with the nurse to see if she should go home, or rest before going back to class. Plus, the kids know the rules..."it's only Advil, who knew they'd check" just doesn't fly.