As an observation, there is not much to explain here; however, the observation certainly brings to light several questions that could be better answered through scientific investigation. It is completely possible that the health link being observed has nothing to do with the milk at all, but the only way to know for sure is to set up a scientific investigation in which the only variable being tested is "real" milk versus formula milk.
What the writing prompt is beginning to explore is the idea that there are health consequences from using formula. These consequences not only exist in cows, but human studies have shown that natural milk provides many health benefits to developing babies that formula milk simply can't compete with. An advantage to the natural milk is that it contains the proper nutrition for that calf in the correct proportions. The mother's milk also contains antibodies, and this is probably the most applicable information for the writing prompt. Antibodies help fight off disease-causing viruses and bacteria. The diarrhea in question could be caused from a variety of things, but it is most likely being caused by a viral infection or bacterial infection. The natural cow milk will contain antibodies produced in the mother's body that are then secreted into the milk. These antibodies help protect the calf from invading pathogens that cause diarrhea.