here is the policy as listed in the GSS:
The taking of prescription medication is the responsibility of the individual taking the medication and/or that individual's parent or guardian. A Scout leader, after obtaining all the necessary information, can agree to accept the responsibility of making sure a Scout takes the necessary medication at the appropriate time, but BSA does not mandate nor necessarily encourage the Scout leader to do so. Also, if your state laws are more limiting, they must be followed.
So let's say that state law does not prohibit someone else dispensing it. Wha