It is between the lines everywhere.
For example, the regs for the epi-pen require a statement of lethal necessity.
If you look at the documentation and security requirements for the health office, “carry your own set of one of the most abused meds by minors” isn’t going to fly.
Even when you look at self-administer, it does not say self-carry.
A child may still need to go to the health office to get their insulin, even if they administer it themselves.
In the end, each school’s liability insurance is going to tell them how to proceduralize the law.
As liability claims keep happening, so will the procedural requirements of each school.