These are questions worth asking and answers worth hearing, but the problem with the question here is that the rule "no vehicles in the park" already comes with a lot of baggage. For example, it's obvious that the rule is meant to prevent driving engine-propulsion vehicles through a park (a rule that we've seen many times in our own parks), so naturally police cars and ambulances will (or should) be exempt, especially if trying to save a life. Otherwise the corollary would be that saving a life is less important than the rule "no vehicles in the park." Which most would very obviously disagree with.
I like the idea of the website, but there's probably a better way to convey the complexities of rule-making and rule-following in the context of both our own moral (or religious, or ethical, etc.) frameworks and the social environment at large.