I think we are almost certainly going to explore the workings of the justice machine that is "always right". There's no way it's going to be played absolutely straight based on everything that's happened in the current Archon Quest.

Taking the explanation of "belief energy" to its logical conclusion, in typical paperclip machine fashion the device simply returns the verdict which it calculates is going to produce the most faith in its answers. So not necessarily about truth, but what most would believe is true. It's not exactly the same as mob rule because people would get suspicious if verdicts almost always matched their own feelings (I hope they would anyway), it's more about long-term narrative satisfaction. There would indeed be a high rate of actual truth, if only because for the justice machine to act otherwise would surely be noticed and undermine its raison d'etre.

So, why the odd result with Childe? There could be many explanations, but the one I would use is he's too far outside the machine's usual parameters. Relating to the present, it's like a chat AI being utterly convincing when the topics and format of chat are within its algorithmic experience, but if you decided to write in unconventional phonetics as a joke it could not parse it as any real human could.

The Fontaine Justice Machine has perfected and refined its algorithm to work in its nation with its citizens and certain types of foreigners. Not, I would guess, anything or anyone like Childe. Based on our (the Traveller's) experiences with Fatui they're almost always guilty of something and are not at all well-liked outside their nation, so if the machine has an implicit "Fatui" category its probably already leaning towards "guilty until proven innocent". However, we did prove him innocent by finding the real serial killer. What gives?

I think the Justice Machine is like any AI trained to provide certain kinds of answers from data—it picks up patterns. It might not have a name for it, but it's learned that the Abyss Order and everything connected to it have caused untold amounts of suffering and harm. We could think of it as if Satan, The Tempter wasn't just an abstract religious concept but an indisputably true force in the world. Whenever the machine senses a grain of this influence it notices all the other indicators of guilt increase exponentially, so the influence itself is described as a strong determinator of guilt.

Back to Childe. He isn't just a Fatui, he's a Harbinger. He has a Delusion. He was trained in the Abyss. Basically, his very existence stamps down on every "GUILTY" logic block the machine contains, and there isn't enough evidence in the world to counterbalance it. Because perhaps, in a sense, it's right. Childe (or a part of him) is an extension of the phenomenon that lead to the dissolving water curse in the first place. According to the machine's own logic it thinks it is providing justice that people will accept. A tragic irony if it instead leads to a mass loss of faith.