As part of OWL training this past Saturday, the council staff suggested that each Den Leader have on hand a copy of a current Class 1 Class 2 physical "just in case", and that the copies go on each and every Webelos outing.
I don't think privacy is an issue since scouting, and activities, are voluntary. It is a one-sided situation ... if you want to participate you have to follow BSA rules.
Regarding meds, the word was "follow the public school", which in this state means that if a medication, either an Over The Counter or a medical Prescription, is given at 'school' it MUST be listed on the child's medical information card without regard to who administers it on 'school' property.
So, if a med is given at scouting, it must be listed.