This is a common misconception of a conventional farmer who isn't truly educated on how an organic farm operates. Cows are an extremely valuable asset to organic farmers just as much as they are to a conventional guy like this one. Therefore, organic farmers strive to prevent any illnesses by always ensuring cows are in a comfortable, healthy environment, have an extremely well balanced ration of feed being fed to them everyday that doesn't push production- rather it provides the best nutrition possible. Just by feeding cows differently (grazing, forage based diets, etc) the organic farm sees far fewer illnesses in cows than conventional.
In addition, the fact that this guy told you that he wouldn't be able to treat a cows if she becomes sick and that she would have to suffer and possibly die really makes it clear how uneducated he is on organics. We DO treat our cows promtly as possible with the onset of illness. We just have different ways to treat illnesses when they arise with natural and organic methods. There are also some approved antibiotics but our with holding time is double or triple what it would be for a conventional farmer (meaning if a conventional farmer needed to keep her out of the milk tank for 5 days, we would need to for 10 or more). In addition, as a very last resort we will treat with antibiotics and sell the cow to a conventional neighbor because we can't make her organic again. It's very rare that a cow would go to slaughter because she got ill. If an organic farmer had a cow so ill he's sending her to slaughter for an, the conventional farmer would likely be doing the same thing.
By the way we have been organic farmers for 13 years as of this Feb. We have had very few instances where we have had to cull cows because of illness and we have had less than a handful that I can remember that needed to be sold to the neighbor in the last 5 or so years (serisouly). Bottom line illness is rare on an organic farm, this is contrary to belief but it's what we and many of our organic friends after transition from conventional to organic.
Hope this clears some things up...