I never liked a rare or medium rare after articles about ecoli and nastiness about meat.
But I do remember one talk where a brother went into this saying that the juices from meat aren't really flowing blood as you would consider it in the veins and arteries and if you properly bled the meat you would still have juices left in the muscle tissue.
I guess the consideration is that when an animal is killed for food and all reasonable measures are taken to bleed it properly then it's okay to eat eve if there's residual amounts of blood still left in the meat.