AE, at home my mother also stores eggs outside the fridge. in the summer it is much hotter than here. i have no idea how this stuff can last. i put eggs in the fridge straight away. sometimes i get huevos criollos here: duck, goose and guinea. they are really great but highly suspicious. i put them inside a pot with water to check for floating but still i prefer to fry them rather than boil.
easy test...drop eggs in water in a pot. if they sink, horizontally, they are fresh. if they stand vertically, on the pointy end, they are usually more than 3 days old. if they float, ditch them.