Okay, this has to end. Anuiel-Sithis.
And yet,....somehow...life goes on.
Of course it does. It's just to much fun to give up.
If Oblivion stayed true to the Lore, then the Dark Brotherhood would have been following Mephala, not Sithis. What they could say they are is that they are tools of Sithis. Tools of Limitation and End. Almost as if they were Sithis themselves. That is why they could keep the name the Black Hand. However, the whole reason behind their murdering goes completely against lore.
As it was said before, Sithis is an ideal. A name given to personify and give a measure of undertanding to something that is complex and hard to understand. Sithis is endless nothing. Sithis is limitation. Sithis is the opposing force of Anuiel. Without Sithis, there would be no world. There would be no universe. That is why the Dark Brotherhood should be so valued in an Elder Scrolls game.