I think it might depend on your hair/skin pigment. If your hair is dark and your skin is very pale, even if the hair is cut a short as it can be, you'll still see it. If your pits are quite concave, it is hard to get a close shave.
When I shave my pits, I shave down, then up, then sideways to the left then sideways to the right. In other words, in all four directions. I find it gives me the closest shave.