I suspect arrival time is when the a/c comes to a stop (and as you say, engines shut down) where pax can disembark. If there's a customs holdup (arriving at AA's JFK terminal before 6am), or if the jetway is broken or there's not one to run it. it's not the airline's fault.

I've heard that the departure punctuality time can be measured by some 4 measures, chosen by the airlines.