I’d guess the concrete masonry unit (CMU) that is wet, is also unreinforced...probably unreinforced all the way to the top.
Not all cells in a fireplace need to be reinforced and filled solid with grout. The corner unit is probably reinforced and grouted solid, but this cell is probably empty. If so, rain could enter the cell anywhere and run all the way to the footing. When enough water fills the cells, then it finds a crack and seeps out.
The CMU is porous so the water fills the cell a couple of inches and then “wets” the shell (wall of CMU)...thus the darkness.