"What crime?" Crime has nothing to do with it. The Imperial law has nothing to do with it. Laws aren't always right.
Okay, let me phrase it another way. What
wrong did Perennia Draconis commit to warrant her murder?
You believe that Rufio deserves to be murdered for killing an innocent woman, but when the player not only murders an innocent woman, but murders her whole family, you see that as morally ambiguous?
I'd say there's nothing that isn't morally ambiguous about the Dark Brotherhood. They don't just go out and kill, they adhere to the requests of others in exchange for money and valuables.
If someone had paid Rufio to sixually assault and murder a woman, would his actions be morally ambiguous?
In a way, they're a government of the people. They make no judgments. If you want someone dead because he sixually assaulted and murdered someone close to you, they'll fulfill your wish. If you want someone dead because he gave you a dirty look, they'll fulfill that wish too.
You seem to be arguing from a sort of nihilistic Kantian ethical position, judging the morality of the act by the intent, and then shifting the intent to the person who hired the murderer, rather than the murderer himself. But the murderer himself is not without intent. He intends to kill. He intends to kill for profit, which is one of the oldest and most common motives for murder. How is murdering someone for personal gain in any way morally ambiguous?
Whether the Dark Brotherhood murders or not is in the hands of the people.
The Dark Brotherhood is part of the people. They could choose not to act. They could choose not to murder someone who has done nothing to deserve it. They possess the capacity to choose... free will. Hence, they are morally accountable for their actions. Just because someone else paints the target, that doesn't erase the assassin's choice to pull the trigger.
A person is not a bullet. They choose their path.
If no one prayed to the Night Mother, there would be no Dark Brotherhood. There's no good or evil in the Dark Brotherhood, there's just the requests of the people of Tamriel.
There are people in this world who make a living by bringing children and women from poor countries and forcing them into prostitution in industrialized countries. If no one paid these people for the use of their slaves, there would be no six trafficking. Does this mean there is no good or evil in six trafficking?
I understand you are a fan of the DB. A lot of people are. I also understand that the "Don't blame the weapon, blame the person wielding it" rationale is a nice way to RP an assassin, but when players actually start to believe it, something is wrong. The idea that the DB are morally ambiguous just does not hold together.
And Adamus Phillida got murdered because he was a threat to the Dark Brotherhood. Does the player not kill Mankar Camoran because he is a threat to Tamriel? Same thing.
I understand that gives the player motive, but it is not a justification. Mankar Camoran was trying to commit genocide. Adamus Phillida was attempting to stop a group of serial killers from continuing their crime spree. They are not the same.