Many consumers are fixated on cooking the red or pink out of the meat they eat. Yet the red color of cooking meat does not indicate if it is under cooked. If steaks or ground meat are kept on the stove or grill until there is not even a little pink left, the steak and even the ground meat will be over cooked and much tougher. Grass-fed meats, especially steaks and even the ground meat, will be very tough when over cooked. Temperature is the key. That's why there are cooking thermometers.
The reason for the red color is that all meats have the protein Myoglobin in them. Myoglobin is made by muscle cells and provides oxygen transport within the cell. It’s similar to hemoglobin in blood in that myoglobin in muscle is red and gives meat its red color. The red color of meat does not come from blood as there is very little blood left in meat.
Steaks and roasts are sterile on the inside. Therefore only their exposed exterior surfaces may host pathogens. Heating the exterior to 160 degrees sterilizes those surfaces. That's why grilling a steak to an interior temperature of only 120 degrees (rare) can be safe. That's because the exterior was exposed to temperatures in excess of 160 degrees. When grass-fed steaks are cooked to internal temperatures higher than 120 degrees that makes them tough.
Ground meats and poultry are different. Ground meats have mixed the exterior surfaces with the interior. Therefore for safety red ground meats should be cooked to internal temperatures of 160 degrees. Poultry should be cooked to internal temperatures of 165 degrees. Again, overcooking will not make the meats safer but it will make them tougher--even ground meats.
Here are several links explaining this:
Persistent Pinkness in Ground Beef Patties from Texas A&M University
The Color of Meat Depends on Myoglobin from Drovers Magazine
The Color of Meat and Poultry by the USDA