GREY squirrels kill red squirrels but they do so only because they feel threatened by the Red Squirrels or they get into a fight over something.
It's a misconception that Grey Squirrels always Prey on Red Squirrels which is not true and the Grey Squirrel will only fight off the Red Squirrel and Kill the red Squirrel in defense.
Red Squirrels also carry a disease that Grey Squirrels are not as prone too but Grey Squirrels can also carry the disease.