Moreover, his "betrayal" is really only effective because, as Garak puts it, it is something Sisko would have wanted to do. Sisko does not contradict what he says here: he was disarmed by it. If Garak had done something more outrageous, he could not in that moment implicate Sisko in the same way.
But, again, as Green says, that's exactly the problem: he didn't tell Sisko beforehand for fear he'd stop him or at the very least whine and whinge to his face even more than he did anyhow. When Vreenak boarded his vessel and headed for home, Sisko
himself should have approached Garak and asked about extreme fallback plans. War is war.