When I wash dirty eggs before cooking (and they all seem to be dirty lately), the spots under the poop do wash off. It's like the poop dissolved the spots. If you rub enough, you can rub off the spots eventually.
Also, when we dye eggs for Easter, if we leave them in the dye with vinegar, the spots start to peel off. I know lots of people who dissolve shells with vinegar before they pickle their eggs. Supposedly, you can even dissolve the shells off an uncooked egg. I've never tried it, but I've seen science activities for kids where they do that.