Fish rots from the head. The Admiralty is the top of Starfleet. They give the orders and directives. I was making the bigger point that Admirals in Starfleet are shady when their is no galactic war going on. During such extreme circumstances like the Dominion War no one (we the audience) should act surprised the Admiralty signed off on and or approved questionable actions by Section 31 in the dark out of public view.
Quoting Odo from DS9 "Dogs of War": "Interesting, isn't it? The Federation claims to abhor Section 31's tactics, but when they need the dirty work done, they look the other way. It's a tidy little arrangement, wouldn't you say?"
We shouldn't be surprised by Admiral Marcus' actions to start a war with the Klingons using John Harrison. While I don't fault the everyday officer. You look at captains like Sisko, Picard, The Kirks, Jellico and Maxwell who have all been on the front lines when the shit hits the fan and compare them to the admiralty they serve under and you have wonder. Is there a culture of doing whatever is dictated necessary to protect Earth and the Federation in the admiralty of StarFleet? In DS9 Admiral Ross retorted Inter Arma Enim Silent Leges, "In times of war the laws falls silent" to Bashir when he was confronted on his actions. You can make a case that the Admiralty of StarFleet operates on that principle in war time, and another latin phrase in peace time. Si vis pacem, para bellum, "If you want peace, prepare for war".