If you want anecdote: I worked on a special farm for one year. (Because it was specialized into grain development, it was smaller than usual, only 5 to 6 hectares). It was also not a standard organic farm, but an anthroposophical one. They practice “biologic-dynamic” farming, following the method described by Rudolf Steiner in a series of lectures in the 1920s. Steiner was a bit out there, getting interested in Theosophy first before founding his own brand, Anthroposophy. Basically he was getting wisdom from visions, not from science, so phases of the moon and mystical properties of cow horns play a role, which is not the norm for the average organic farmer. (The farmers were also against unneccessary vaccinations in humans because of the anthroposic beliefs, along the line “Tetanus can kill you, so yes to vaccination, but measles are only a children’s disease, so lets skip that”. Lets not derail this thread, I’m just recounting.)
Since the farm was so small, we only had half-a-dozen chickens for private purposes, and none got sick. The cows were also generally in good shape - the good handling was also part of this, like taking a few minutes more during milking to prevent mastitis - , but when they had problems with the hooves, of course the vet came. A normal, state-appointed vet. He prescribed medications necessary, but because of the ideological framework, things like Bach flowers and homopatheic medicine was choosen first. If this didn’t work, then stronger medication was used.
It’s important to remember that antibiotics are not a cure-all or go-to-first choice either in human or animal medicine; with the increasing resistance, in human medicine trying other options so the body immune system can fight it off and saving the big guns last makes sense. And a lot of diseases are treated with non-antibiotic medicine routinely, anyway.
As for your apparent problem with “no antibiotics in the meat” a contradiction or misleading if “animal receives antibiotics in case of serious illness” - that’s why there’s a long waiting period for milk and meat after medicine is given. The vet and animal science knows how long stuff takes to pass through the animal, and then a safety margin is added. This isn’t like Dioxin or the poly-chemicals which are stored in body fat and thus remain there; they pass through and then the meat is “free” again.
Don’t forget also that in order to keep their certification, organic farmers in the EU are visited by a controller once a year, plus a visit from a seperate person from their organic group.
And some of the organic companies that process the meat, milk etc. also conduct random lab tests to be sure that the farmers keep their word and don’t scam the higher prices.