Japanese trains are famous for being never late. The only exception is when someone tragically chose train tracks instead of a tall building. That's undoubtedly what happened in this chapter if the train was full 15 minutes late.
That being said, it's sheer folly to plan your schedule to depend on single minutes if you are travelling any significant distance (let's say a distance you won't walk leisurely in short time). If an event starts at 14:00, plan to be there 13:45. If these folks had done that, even with their delay, they would have arrived at 14:00 and not been late. If there had been no delay, waiting 15 minutes outside would be no big deal; there was no blizzard or monsoon going on.