It’s come to this. I’m posting pictures here to win an argument on a message board.
In a discussion on WoW Insider (posted here) I mentioned that it was weird seeing Draenei wearing Ten Storms (and the BC recolored pieces, which are listed in the above post) since TS is covered in Horde logos. Admittedly, I was referring to the Horde logo from Warcraft 3 (seen here) and not the updated one for WoW (seen here), but it’s clearly nearly the same logo.
However, the symbol may be a shamanism symbol that the Horde adopted for their use. Note the wolves on the WC3 crest.
Either way, it still says “Horde” to me.