This is true for my flock too. Sometimes very poopy eggs, MUCH dirtier than the ones in the picture, are feed back to my flock if I don't feel like cleaning them that day. When I have one of these eggs, I bring it into the run and everyone gathers around. If I throw the egg to the ground and it doesn't break, all the chickens stare at the egg and then at me as if to say "why are you throwing our eggs around Mom?" If I throw the egg again and it breaks, they turn into a school of piranha, devouring the egg in seconds. Only broken eggs are consumed. Even shell less eggs are left alone if they are intact.
We refrigerate all eggs unwashed unless they are pretty dirty. If dirty, we rinse them off in water warmer than the egg before refrigerating. We do rinse eggs before using.
We get some flooding from heavy rains and wind driven flooding. I would not recommend gravel or sand. The poop will not break down and the gravel will start to reek. We had sand in our original set up. After two years, it smelled so bad we had to remove it. We spread it out on the driveway and it continued to smell for months