In short, it doesn't.
There is some saving grace though for the arc in that I could imagine why people in universe would think it does. Remember we have what Riker's holodeck would call Objective Mode. We can see both sides of the conflict, and also see the truth of what happened when Burnham and Georgiou beamed over to the Ship of the Dead.
From the in universe perspective of somebody on the Shenzhou, they encountered a Klingon device, Burnham was in some kind of vaguely defined conflict with a Klingon in a spacesuit, then the ship is confronted by a Klingon vessel, and while the captain is preaching peace and calm, Burnham apparently goes nuts, argues with the Captain, then decides to mutiny in front of the bridge crew, then gets given a second chance and beams over to the Klingon ship with the Captain she just metaphorically stabbed in the back, then comes back unscathed with a story of how said Captain literally got stabbed, and the mission failed by Burnham's hand. Then their ship and all the others got blown up.
I could see how the characters might interpret the resulting war as Burnham's fault.