One of the keys in figuring this out is the brief showing of Covenant in the H4 demo. Notice the Jackal that is with the Elite. No known jackals ever joined the Separatists, which means every jackal and elite were on an opposite sides of the war. This means more than likely this is a splinter group or even an outcast group that is stuck, possibly never having even heard of the Separatists. It certainly would explain the more cut-down look of the elites. Then again, Jackals are mercenaries, and possibly just being payed to work with elites again, but I find that to be a very unconvincing reason.