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I heard in a recent shiur that Dayan Weiss zatzal ruled that an animal that delivered its young via caesarean section is considered a treife. Therefore its milk cannot be drunk. When supervising milking the shomer checks that any such animals are locked away before milking.
How do those those who permit cholov akum put up with this possibility? Is it through bitul?
R Asher Weiss has a teshuva on a similar topic (Shut Minchat Asher, vol. 1, page 126). He answers how one can drink milk from a herd when one knows statistically some of the cows will be tereifot.
He explains that as long as the majority of the cows are kosher, the statistics of what percentage are really tereifot don't matter. Specifically he writes that even if it is true that from a statistical probability it is impossible to say that all cows in a herd are kosher, we can rely on the concept that this herd follows the general statistics of the average number of tereifot in a herd. From a din Torah perspective, every cow has the presumption of being kosher (since statistically more than 50% have been found to be kosher), thus even when bringing many of these cows together, they are all kosher from a Torah perspective.
I see now that Halachipedia mentions a similar argument but see there for other arguments.
Rav Asher Weiss (Minchat Asher Shemot siman 43) argues that principally we view each cow as kosher because of kol d’parish m’ruba parish and even when their milk is mixed up the milk from each cow retains its kosher status despite the overall statistic. His primary argument is that once we have a halachic principle to state that the milk is kosher the halacha ignores the physical reality or statistic. One proof for his argument can be derived from Gemara Zevachim 73b which implies that once the principle kol d’parish m’ruba parish is employed even if the items are later mixed up, the remain kosher. Another proof is the Rama who states that the cheese made from many unchecked cows who were only considered kosher by merit of a chazaka remains kosher. This gemara is cited by the Rosh (Chullin 7:37) for a similar point.
I also see R Michoel Zylberman from YU's Kollel wrote an entire article on the topic in the Journal of Halacha bringing different proofs and concluding with the reasoning above. See especially pp. 106 and following.
I'm not sure that all Cholov Yisrael dairy producers do this; there have been a number of questions in the past about whether many dairy cows are treifa.
In a theoretical sense, we know that some dairy cows -- let's say more than 1.6% but less than 50% -- are treifos. If I have one cow on my farm, Bessie, then rov says assume Bessie is kosher, so Bessie's milk is 100% kosher. Okay I walk into a modern dairy setup with a thousand cows' milk all mixed together; if 4% of those cows are treifa, does that mean my milk is 4% treifa and 96% kosher? If so it's not kosher! Rabbi J. David Bleich writes about this in Tradition Spring 2008. The answer seems to be based on a ruba de-leisa kaman. If I don't know that any particular cow on my farm is treifa, even if I know that the general population in theory has a 4% treifa rate, then I assume each of my cows is 100% kosher, and thus the milk is 100% kosher.
So your question would only be if a mashgiach walks onto a dairy farm and knows specifically that there are one or more treifa cows here. Which I doubt is usually the case in industrial-scale chalav stam production.
From the Chashash Terefa point of view, the unsupervised milk is better. Because nobody would try to check if a cow is Terefa. Even if they decide to eat it, the non Jews would not verify if the animal is terefa. So we have both Chazaka and Rov.
The first is Chazaka, Milk cows are greater than one year, so they wasn't terefot when they born. The chazaka is a Chazaka demeYkara. This point is a Machloket Rishonim in Gemara Chulin 11a. See Tosfot paragraph Atia. Tosfot rules that this Chazaka is not valid because the non-terefut was not clear at time. We know that the cow wasn't terefa before 12 month because a terefa cannot live 12 months.
Even if the Chazaka per se is not valid, we have a Rov. Most animals are healthy. Moreover, Rav Shimshon bar Shimshon says there is a Chazaka that come from the strength of Rov (he think that Rov is a Berur equivalent). That is, even if a cow becomes Terefa and you have cheese from it, Rashba (there) says that from the strength of the Chazaka we say that it became terefa after the confection of the cheese.
Anyways, in non supervised dairy, there is no case of discovery of Terefa. Even more, if it was the case, milks of all cows are mixed and Zil batar Ruba, the mixture of Chalav Terefa with a majority of Chalav not Terefa is cancelled.
