I don't doubt they would have but they would have still be wrong, just as they are now.
Unless we have proof they weren't even being reminded to drink water/wear a hat then we cannot call them negligent.
Reminding is not enough. Active supervision is what's missing. I've said it several times, but you don't want to read or process that bit.
What if she'd run into the road? The teachers would be watching them, they would be told not to do so, those who would be more at risk would be kept by a teacher/adult and on the inside. It still doesn't prevent a child doing something stupid they should know better on.
Would you call them negligent then?
No, because in the example you've given the adults are taking active measures to ensure compliance (teachers watching, keeping children at their side etc). In OP's daughter's situation this was not the case, that's why they are negligent in this instance. If a child had run in the road because the teachers had issued reminders and nothing else, and assumed 'well they're 8 they should know better', then yes, they would be negligent. In the same way, if the teachers here had actively ensured all the children were drinking and wearing hats, not just reminding, then there would be much less grounds, even if the outcome had been the same.
The cases are very different and cannot be judged in the same light - not every adverse outcome should be classed as negligent, however this one, based on the facts we have, was.