So anything we do is justified because everything the other side does is also wrong? Because you're missing the point of why this matters, which you can find plenty of examples real life and it would have nothing to do with New Antioch. It's wrong because you're sending the people of Aqua Palma to war under FALSE pretenses, to fight and die for you based on a lie and a crime you actually committed!? The concept of an illegal war matters for the one who declares it, it has nothing to do with what New Antioch is but his responsibility as the leader of Aqua Palma. You can lie and make up whatever you want, justify it however you want, but that's the truth, you're sending your people to kill and die on false pretenses. Look what it's doing to the tavern lady, who just wants her normal life and peace and stability back while being tormented by the truth and fear of what they're doing, including getting into bed with the same Criminal group that massacred your miners to begin with!
Your belief really doesn't matter against the facts. And the fact is if the brother had never blamed the MC for their Dad's death, MC could have easily gotten into New Antioch without that made up story. He wouldn't have been arrested, he wouldn't have been thrown into the dungeon, and he wouldn't have been almost executed. He probably wouldn't have even needed to sneak into the city, because New Antioch has free travel. Maybe Faustina might have secretly assassinated him (which the MC wouldn't have known at that time) still if she knew, but she'd never have the justification for a public execution and forcing the MC to fight for his life in the arena. The only reason to use that crime/cover story is to kill the MC, there's no other purpose for it and your belief doesn't change that.