This is actually a principle strengthen question, which is really not different from a standard strengthen question. However, they do generally tend to straddle the line between strengthen and strengthen with sufficient- and this one is in fact asking us for something that "justifies" the argument.
Either way, I don't think this will actually change your approach. The answer will be a general principle that, if applied to the scenario above, will make the argument better, and likely make it entirely correct.
