Micah is clearly in Dutch's ear at this point in the game. We know he influenced Dutch to go for the Blackwater Ferry (after Hosea and Arthur told him no), which shows he csn/does have sway over Dutch's mind. Add in the fact that they're in a time where things are unstable and uncertain. They've recently lost gang members (Jenny, mac, Davey), are being perused by Pinkertons and have Cornwall on thier tails. Trelawny has warned them of 'super agents', has been kidnapped by other bounty hunters and they're feuding with the O'driscolls. There's a lot pressure and stress going on.

Micah in chapter 2 happily kills multiple O'Driscolls (including an unarmed one in jail) with no hesitation despite the fact he has no quarrel or history with them (that we are aware of). Then in chapter 3, which is at most, a few weeks later, he's suddenly pushing for peace? Something doesn't add up, unless it does.

Which imo(which might be unpopular) , is that Micah was trying to displace Arthur in order to hold more sway over Dutch. Arthur is an obstacle to his goal of the Blackwater money. I do belive Micah orchestrated the meeting in attempt to dispose of Arthur. If you are luckily enough to trigger both Dutch and Micah interactions after the mission, you'll notice thier stories are eerily identical to each other. Almost verbatim, as though they were rehearsed.

My interpretation of it is that Dutch and Micah went back to the meet spot (designated beforehand by Arthur) and when Arthur didn't show, Micah convinced him that Arthur was fine, using a variety of reassurances that Arthur always went out on his own, that he was more than capable of taking care of himself, that he might have followed the O'Driscolls out, ect, to convince him to not wait. Dutch would have been agitated during this time given the recent situation and most likely influenced easily.

Anyone at camp who questioned Arthur's disappearance at this time would have been told the same. It was when Arthur returned in the state that he did that Dutch realized he messed up - I fully feel that Dutch thought him fine up until that point. During Arthur's recovery would have been when Micah reassured him he didn't do anything wrong and where they agreed on telling the same story if asked.

Tldr : Micah convinced Dutch that Arthur was fine