The key here, as all we forget from time to time, is that we don't know what the Reds' scouts saw prior the trade. We really don't know what the Reds expected from Broxton and why, so it's difficult to for us as fans to assess the logic side of things.
If they come out and give us a "we like Rheal Cormier because of his low ERA" type of explanation, I see no problem with us tearing that apart. And I tend to think that the explanation you provide above is fairly accurate. But I don't think we should dismiss the possibility that the Reds projected Broxton to be more effective from a K:BB standpoint for the rest of the season than he had been to date.