An egg thread, and I haven't contributed yet!! My excuse is that I have been out of town.
I have about 30 hens, and I worked for a while as a poultry grader, grading eggs and chicken.
Commercial enterprises do wash the eggs, and washed eggs must be refrigerated. Unwashed eggs will last an amazingly long time in a cool place. My eggs always seem to be dirty--maybe I need to tidy up the hen house.
When you wash eggs, wash them with a drop of dishsoap and WARM water. Sounds counterintuitive, but cold water makes the eggshell contract, which may draw bacteria into the egg.
If you have fresh eggs, and you want to make hard cooked eggs, you need to wash the eggs and then let them sit in the fridge for at least a week. Fresh, unwashed eggs will NOT peel.