I believe that there is something to it. Some cows will develope a disease called “bloat” which can be fatal. The veterinarian will perform an operation on these cows. According to the OK website “There is a medical operation performed on cows that punctures the fourth stomach wall, or abomasum, rendering the animals and their milk not kosher. Mashgichim have to ascertain that these cows are separated from the general population during milking. (This is a concern for chalav stam as well; how we address it there is beyond the scope of the present article.) Before our most recent production of chalav Yisrael, we had Rabbi Dovid Steigman, an OK Rabbinic Coordinator who is also an expert shochet, inspect the animals to insure that no operations had been performed on them.
My mother-in-law, who was raised catholic (my husband a’h was a ger) can only drink ‘Jewish Milk”. (By the way, we had discovered that she had decended from Marranos on her mother’s side…)