I don't think the dirt has much to do with the state of the hen's butts but the state of their feet
I guarantee it can be the state of their butts. I had a hen that smeared the eggs with poop. I noticed she had poop all over her butt. I had to wash her butt. I swear it was the most awkward thing I did to a chicken, especially because she really enjoyed it. Solved the problem though.
I'm in the U.S., and the big caveat that I seen with places that wash/don't wash is that those countries who don't wash vaccinate their chickens for salmonella.
Washing eggs is irrelevant for salmonella. Chickens infected with salmonella has it in their oviduct, and the bacteria is literally embedded in the egg albumen. So if the chicken is infected, it will lay eggs with salmonella already inside it.
See 4:00
Our world, our bodies are covered in bacteria. We have more bacteria than our own cells inside our bodies. 99.9% of bacteria are harmless, and many of them are beneficial, like probiotics.
Probiotic and lactic bacteria inhibit the growth of harmful bacteria.
When an egg is laid, it has the bloom to protect it, but it also has a biofilm of probiotic bacteria from the chicken's gut, most of which are beneficial.
When we wash the eggs, not only we destroy the bloom, but we also disrupt this ecosystem of lactic bacteria and probiotics. When good bacteria are destroyed, we make space for bad bacteria to take over. Washing and disinfecting cause more harm to the good bacteria and very little harm to the bad ones, which can freely reproduce with no more inhibition from the lactic bacteria.
Proof is that washed eggs rot even when refrigerated, unwashed eggs do not rot even at room temperature.
Microscopic ecosystems are extremely important for our health and our environment, unfortunately this theme is not only misunderstood, but almost inconceivable for regular people.
The more sterile we make our environment, the higher are the chances to have an extremely bad bacteria harming us. It's not by chance that the most catastrophic infections happens in the most sterile environments - hospitals -.