The eggs came with this note: "since these are washed, you'll want to store in the fridge". This raises two questions. First, washed? Second, when wouldn't I store raw eggs in the fridge? I always do, so this note puzzles me.

Birds only have one hole back there. Eggs in their natural state come out covered in shit. They also have a natural protective layer that keeps them from rotting fast at room temperature.

In America - but not, say, Europe - eggs are habitually washed for sale. This removes the dirt, but it also removes the protective layer and makes it unsafe to keep eggs out on a shelf. If the eggs are unwashed they are safe to leave out, and often it is considered safer to leave them out because moving them from refrigeration and then back out again can cause condensation to develop which is extremely likely to encourage rot.