To my great delight, the answer was in the extras. For while that was the only episode of the original series on the disc, there also was an episode of the animated series, "More Tribbles, More Troubles" with commentary by David Gerrold, author of both episodes. And, the DS9 episode "Trials and Tribble-ations." This last, to bring the story back to where I started, was mentioned on Big Bang Theory and I thought they must be making it up, until oidhche and palingyuan set me straight.
This, my friends, is how the world is supposed to work. Extras don't have to be crap.