Why is everybody obsessing over whether Eb had permission in Changes when he went to town against the Reds? The fact that Eb was the blackstaff is ONLY relevant to the extent that he used death magic to kill those human guards. But if Eb had limited himself to targeting Red court vampires or disabling humans, there is no issue.
The White Council is not like the CIA or FBI. It is not an agency with a centralized command structure and wizards do not routinely act on orders. It is much more like a fraternity which gives its members broad freedom of action within very rigid boundaries set by the laws of magic, the rules of the White Council and the treaty obligations like the Unseelee accords. Harry has gone out and killed loads of supernatural bad guys without specific white council permission - or the expectation that this permission was even expected. The organizational culture of the WC was set in medieval times and probably resembles more an guild of master craftsmen or perhaps a conclave of nobility than a modern corporation, army or government organization. It is a group of independent and powerful peers, not a strongly hierarchical organization.
Since the White Council is at war with the Red, any wizard is pretty much free to attack the Red Court whenever and wherever they wish -- provided they do not otherwise break the laws, accords or other white council rules. They White Council would "prefer" you coordinate your actions with their wardens as that makes the WC as a whole more effective. The wardens are often given orders like soldiers, but I suspect even wardens are not expected to "only" attack the red court under SC orders. Eb is not a warden, so even that restriction does not apply.
My personal opinion is that the WC restrictions on the Blackstaff are more strategic than tactical. The WC may point the BS at specific problems. The WC may censure the BS if the BS goes to far or abuses the position. I imagine the BS position could be revoked if abused, but I doubt that has ever happened. I imagine that only the most trusted of wizards would be allowed to take that position.
That said, I do think Eb might be the most powerful Blackstaff since the original Merlin (who is suspect was the first). Blackstaff and Senior Council member -- that is a very powerful combination.