Arsenal were last promoted when the football league was resumed after the first world war 1919/20. The previous season, 1914/15, they had finished 5th in the 2nd division behind Derby, Preston, Barnsley and Wolves yet were still promoted in front of Barnsley and Wolves, who had finished higher.
I assume some sort of dirty dealing went on behind the scenes. They've always been a cheating bunch of barstewards.