Both Bull and Solas indicate that the Qunari are naturally a savage race, with the Qun functioning to counteract those natural impulses. It seems quite possible that the Kossith are just as savage, but perhaps have a society that embraces that.
Maybe.
I took it as meaning the Qunari, after becoming more draconic in some way, became more savage and different than the Kossith, so the Kossith drove them out, then the Qun came into the picture when the philosopher was trying to figure a way out to survive, and then they became the Qunari.
I don't see how the Qunari "had to leave" as Bull says if they were initially no different from the Kossith, and it sounds like the dragon stuff is something that came afterward.
Edit: Kieran (morrigan's son) commented on my qunari's blood which was interesting. He said he noticed my blood first, but was still a little surprised that I was qunari, which made me think the qunari are an altered species or something. Then again, maybe you are right that it is actually in reverse to what I said or something, which is why the Qunari like seeing Qunari without horns or something.