I think it's some kind of crazy-weird thing about staging the release of kids -- cars, then buses, then kids walking on their own -- as a risk-management thing. Without knowing what the layout of the school and its surrounding areas are, it's hard to say whether this is called for, but it would be pretty extraordinary if the situation was so terrible that kids leaving the school on the sidewalk were at risk from cars or buses in the road.
I think these parents decided that they didn't want to spend over an hour in a traffic jam (which they described as a danger; again, hard to say whether an hour-long tailback is a danger or just a titanic pain in the ass) so they walked in to get their kids.
They're arguing that the "walking kids leave last" policy is about kids walking without parental supervision, and asking that their kids be handed over to them immediately, rather than waiting for all the cars and buses to clear out. Officer Powertrip is insisting that there is no category for "kids with parents" and that any kid on foot leaves the school only after it is clear of vehicular traffic.
That's what all the business of citing state law about turning kids over to parents in a timely fashion is about.