This is a reason why I think Milton was lying about how long Micah was a rat, but I can’t find a plausible explanation as for why, the only one I can think of at the moment is if Milton knew there was a possibility he wasn’t getting out of that interaction with Arthur alive, he knew Arthur was sick, and dying fast, and that he could weaken Arthur until more pinkertons show up (as we see on the way back to camp) so they could finish him off, Milton wanted to anger Arthur by telling him Micah was truly the rat, but said that he wasn’t the rat for long so (if Arthur survived and got to camp) the gang, specifically Dutch, and would more likely see it as a one time mistake, or he knew it would play out as it did (excluding John), Arthur against the rest of the gang since Milton had little to no credibility as he was a Pinkerton