That's nitpicking. Of course the story is contrived. If you can think of a more plausible premise that would have had the same visceral punch and been easy enough to understand, speak now.

The point of the story is that sometimes there's just no good way out of a situation, and the thing to do is face up to this and deal with reality on its own terms. Safety labels and supply closets are only incidental to this message. It could just as well apply to ugly tribal wars, or to medical triage, or to the fact that few things worth doing are perfectly safe.