I think it's more nuanced than that. The Hound was currently on trial--being bound and accused by the BwB and already defending the charges against him. Arya stepped in with this additional accusation--that the Hound killed her friend, the butcher's boy--this additional evidence of his crimes. I would say that she is more of a witness to the court, already convened.
BwB were essentially accusing him of crimes committed under defense/orders of the crown. Technically, these would all be legal from a feudal perspective. BwB are a loose organization with its own rules, their own common code, I suppose--so the crimes of the Hound speak to a common morality that is made legal by the crown--which is why the BwB exists in the first place. Still, they organize among the same principles as the law, and even improve upon it--convening the trial, based on accusation and crimes committed, allowing the accused to answer to all charges (something that Tyrion seems to be denied), and granting the trial by combat.
But Arya's was the accusation that eventually damned him and forced the combat, so I can see it that way. It's important to note that he was already wanted by the BwB, and they were already trying him.