I believe I understand a little more about the flora that lives in ones gut than you give me credit for. It is my job after all to tend to people with GI bleeds, colitis and the like. My bible based beliefs also give me sound doctrine concerning the consumption of blood.
Blood flows through the circulatory system. It does not reside in the interstitial spaces. The red color of blood comes from Hemoglobin, the protein in red blood cells that allows for the transport of oxygen from the lungs to the body's other cells.
The red color in meat juice comes from Myoglobin, the protein in muscle cells that enables the cells to transfer oxygen from the red blood cells and into the other cells.
These two proteins, while working together, are not the same thing.
After an animal has been butchered and drained of blood, the meat is Biblically considered to be free of blood.
When squeezed out of the raw meat, the fluid contains Myoglobin, not Hemoglobin from red blood cells.
When cooked, the Myoglobin in the interstitial fluid coagulates, and the meat juices run clear. This is not "blood" clotting. It is Myoglobin tightening up under the presence of heat.
When eating a cooked steak, you are eating everything in the steak, including the Myoglobin and the interstitial fluids.
If it were indeed blood, a steak that had been sitting in the refrigerator for a couple of days would be covered with, and full of coagulated (clotted) blood because there would also be platelets present, basically a big scab would have formed.
Myoglobin is a major source of iron. The meat juice squeezed from raw beef was an easily consumed source of nutrition that a convalescing person in the olden days may have had no other way of consuming. Today we have I.V. solutions that can provide nutrients, back in the early 1900s, not so much.
That 'red stuff' that oozes out of the meat is packed with nutrition! It's full of iron, copper, selenium and other trace elements. It's got potassium and water-soluble vitamins. It's got a large chunk of the special nutritive properties of meat.