I went by frozenchicken's words rather than by my (single-player and replay-watching only) knowledge of Starcraft. "Clearly brilliant yet arrogant" is a lock for Protoss, and "bright but not exactly street smart" cannot be Terran.

Now, chaotic fighting indeed doesn't fit with the Protoss at all. But Hermione's strategy is by far the one that most parallels a hive-mind, and for all we know the semi-sentient Zerg really are all happy-go-lucky on the inside.