this is really quite simple when you think about it. think of both the edi order and the sith as what they really are, a religious cult/organization. think of any of todays religions, if you stop following the teaching of your religion and start following the teaching of another, then you would stop calling yourself a follower of the first religion and start calling yourself a follower of your new religion. your old religion would still consider you a part of their religion, and your new religion would not consider you a part of theirs if you didn't claim to be a part of it.
its really that simple,
No, it's really not
that simple. Keleth-Ur is still considered a sith lord. (He's the heretic with the hologram in the sith temple on DK.) The sith don't call him the 'jedi Keleth-Ur', they call him the heretic sith lord. They are even aware of the general nature of his heresies, but still recognize him as sith.
As far as the religion analogy, it doesn't hold up. Baptists will tell you they are christians. So will lutherans. As will episcopalians. And so will those small churches full of snake-handlers. Most of these churches still recognize the others as 'christian' (misguided perhaps, but still christian). That's why there are no calls for crusades between these denominations. *wink*
Similarly, Revanites in game refer to Revan as 'darth Revan'. I bet if you asked a random sampling of revanites, several would say, ''oh yeah, we're still sith... just a different kind of sith''. These revanite heretics still access sith powers. At least one (the girl that sends you after revan's mask), is clearly dark-side.
So you can SAY it's ''really that simple'' but clearly, it's not. In my opinion (no more or less 'right' than anyone else's) sith are sith as long as they beleive they are sith and can demonstrate a mastery of sith force techniques.