Batman isn't pro-killing or pro-guns but he's definitely pro-not-snitching-on-people-who-seem-to-have-some-kind-of-working-moral-compass-and-also-kill-scumbags! That description of Deathstroke and Vigilante (whose new Secret Origin takes place in this story) makes them sound way better than Gotham Cops who obviously love to kill scumbags but mostly have faulty moral compasses. So I see why Batman doesn't mind letter Douchéstork run around free. If he arrested Douchéstork, he'd probably have to arrest a bunch of Gotham Cops too! Plus Dick vouched for him, so, you know, whatever! I guess Bruce does whatever Dick says, the spoiled brat!