Grass fed meat is unique and needs to be cooked a little more reverentially than grain fed meat. It is a very healthy cut of meat, from a very healthy animal.While factory farmed animals are purposefully fattened, grass fed animals are naturally lean (and healthy). Not only does the fat in factory farmed, or grain fed meat, protect the meat from overcooking, some factory farmed meats are also injected with saline. The saline adds flavor (salt) to an otherwise bland cut of meat, it also adds weight and therefore cost to the consumer. The saline, along with the grain fed fat, keeps the meat from cooking too quickly. It is easy to cook grass fed meat properly, once you understand the difference.
Grass fed animals are raised on pasture and have room to move around so they do not have the excess fat that accompanies factory farmed meats. Grass fed meat tends to cook quicker than grain fed meat and without that protective layer of fat, or added saline- it is easy to overcook.
Like so many things in our modern diet, it just takes a little unlearning. Your grandmother most likely knew how to cook meat properly. "Go Low and Slow" is how my mom described it.
Actually she was talking about how to safely fly an airplane - which we don't recommend- but for cooking Grass Fed Meat, it is very sound advice!