All right, let's look into your interpretation. Instead of 'setting' though I'll use the term 'backdrop' just because that's harder to misinterpret.
So against the
backdrop of the Zerg, who act primarily as catalysts for driving other plots, we have the individual stories of Mengsk's rebellion, Kerrigan's infestation, Tassdara's struggle for unification. OK, let's say we agree.
Fast-forward to Brood War. We have the
backdrop of the UED invasion, and set against it we have everyone banding together with Kerrigan, and Kerrigan playing the different factions against one another.
Fast-forward to Reign of Chaos. We have the
backdrop of the Demonic invasion, and set against it we have (in the last two campaigns) the Alliance, the Horde, and the Sentinels banding together with Arthas (through Illidan) representing the Scourge, and the Lich King through Arthas playing the different factions against one another.
Uh-oh. Seeing a problem yet?
Fast-forward to Legacy of the Void. We have the
backdrop of the Hybrid invasion, and set against it we have the Terrans, the Zerg, and the Protoss banding together with ... who's the wild card this time? Duran? Valerian? Kerrigan [i]again[i/]? Ulrezaj? ...and said wild card playing the factions against one another.
So let's say the Hybrid invasion isn't a story itself, as you put it, it's only the backdrop for stories. Well, as Nicol said earlier in this thread, it just doesn't leave any room for more nuanced stories than the ones that've already been told. As long as you're not
Chaotic Evil you as a sentient character have no choice but to ally against the greater threat, no matter who that happens to be.
This is definitely one of the biggest concerns right now with where SC2 is going. Many of the things that "went wrong" with WOL can be learned from and fixed in future campaigns. I'm not sure Blizz has any intention of preventing this mess, however.