Actually, the beef that we eat is mostly fed a mixture of corn and high carbohydrate grains. You can buy range-fed beef (cattle that eat grass only) and it is very lean; scarcely any fat at all. The last time I looked, range-fed ground beef was selling for about $6 a pound.
It is the high intake of cheap carbohydrates - refined sugar, potatoes, corn, most grains including rice; anything white and is sold in a cardboard box - that is responsible for causing fat in the animal or person eating it.
I eat almost no meat except venison and feral hogs. Last year I even added a roast beaver to the menu (the kind that build dams and eat trees, not the other kind that is normally for desert).
I have to add a bit of beef or pork fat to the Bambi-Burger and pork sausage to improve taste, but it is still a low fat product.