Another (gruesome) thought experiment:
You have a dead body hanging vertically in the air. You cut off the head and feet simultaneously. What happens?
Now you do the same thing to a body underwater. Does the same thing happen?
[I'm going to bed so here are the answers: for #1, the blood all pours very quickly out of the feet, because at the site of the cut, the pressure inside the blood vessel is much higher than the surrounding air, because of the weight of the column of 5 feet of blood. In #2, some blood will dissolve out through the neck and feet, and since blood is very slightly more dense than water, it may very slowly drain out of the feet if you leave it there long enough, but it does not pour out of anywhere. This is because the pressure in the blood vessel due to the height of the 5 foot column of blood is going to almost exactly equal the pressure in the water surrounding the site of the cut, because you have an equivalent amount of water there.
You have to think in terms of what would be FORCING the blood to move. In the case of air, the fact that the 6 foot column of blood - the body - WEIGHS so much more than the 6 foot column of air containing it means that your blood wants to SINK in that column of air. When in the water, the 6 foot column of blood WEIGHS almost exactly the same as the 6 foot column of water containing it, the blood has NO TENDENCY TO SINK.]
BTW, the "red water in a ziploc bag" is a perfect analogy. The human circulatory system is riddled with muscles, valves, and all sorts of other tissue, but the compelling physics involved are VERY well illustrated by the bag. In water, the blood has NO TENDENCY TO SINK because it's the same density as the surrounding water.