Actually, I think that the black marks are mildew. What happens is that water eventually will work through almost any finish and the towel held it there nicely. The first thing that happened to the floor was that the finish turned white as water combimed with the polyurethane. This is reversible without removal of the poly. The next thing that happened as the area stayed moist is that a mold or mildew spore started growing and that was the parent of a lot more of them. The spores are always in the air and will stay dormant for years. One--or a lot more, really--was under the finish. With a host surface and moisture, they had all they needed to grow.
The wood bleach will kill them and remove the black color, but you do have to remove the finish for it to get to the mark. A paint stripper will do this. The mold or mildew isn't acid or basic, particularly, but the strong chemical kills it and removes the color. Be sure to follow all the directions and safety instructions on all the products that you use. And be sure that you read the instructions several times and understand them.