Hi there... I just love barred Rocks!
Let me give you the real down low on egg storage.
Fresh unwashed eggs CAN be stored at room temp. BUT they lose freshness (not the same as rotting) at a rate of 7 times faster than being stored in the fridge. One day on the counter is equal to a week in the fridge. Left longer... as in 3 months at 70 degrees...

the evaporation that takes place makes the eggs thick and sticky inside. Those that had little invisible cracks will be rotten by this time and sticky maybe even oozing.
By this (7 times faster thing) I mean the white and yolk become thinner faster. Which makes them pop easier when you drop them in a pan for frying... making for more accidentally scrambled eggs.
So if you are eating the eggs immediately... counter top is fine. If you want fresh eggs longer refrigerate!
Fresh unwashed eggs stored in the fridge can last easily 6+ months and STILL be better than store bought.

Store eggs are often 30 days old before shipped to market with a 30 day date, returned to get regraded and sent back to market with another 30 day date, then returned and sent out as industrial use for things like liquid eggs in the carton, school lunches, and other industrial uses like cake mixes and such. Though they do wash store eggs, most companies replace the bloom with a thin coating of mineral oil to help reduce air (gas) exchange through the shell and maintain freshness.
My practice is to put fresh eggs in the fridge immediately. They last longer PERIOD. Pointy end down for the best preservation.
Also note some folks think you can't boil and cleanly peel a fresh egg... wrong. The key to perfectly peeled boiled eggs 99% of the time... regardless if fridge or room temp get
water boiling BEFORE you put the eggs in. Salt in the water or anything else is irrelevant and the overall increase in boiling temp due to the addition of salt is between 2-4 degrees. Once you are done boiling
COLD water shock... for me my well water is cold enough but some folks may require ice water. So just remember shock them in and shock them out. It works every time. So if it isn't working you may not be getting them cold enough or for long enough. This method changed our boiled egg life!
If an egg gets mucky and I decide to rinse it off with water... we usually use those first or scramble and feed back to the animals if we are egg rich.
Hope this helps.