I wouldn't say it's a myth, but the farmer does have a point to a certain extent. Modern dairy cow breeds have mostly been selectively bred to produce large volumes of milk with grain supplementation, they're genetically programmed to do so and will often make milk at the expense of their body tissues (become emaciated) if they don't get the concentrated calories provided by grain. It takes a specific set of circumstances to keep them healthy on forage alone (meaning pasture and hay) - the genetics of the cow, the quality of the forage, the season, etc., are all factors. Some dairies do feed exclusively pasture and hay, it can be done, but it is usually seasonal, with the entire herd dried off during the pasture's dormant season, requires excellent soil and management-intensive grazing practices. Generally speaking, you can't take any ol' dairy cow of the major 3 dairy breeds (Holstein, Jersey, Guernsey, the last 2 are vastly outnumbered by the first in the US), feed her only pasture or hay and expect her to stay in decent condition during the height of her lactation, when she's producing many gallons of milk per day. There are exceptions, but it's not the rule with what farmers in the US these days have to work with. Some other countries have more of a pasture-based system of dairies, they seem to have it down better, with different cow genetics and farmer knowledge base (New Zealand, for instance).
