Imagine putting your wrist up to a neck wound gushing with blood. What angle is your arm at when this happens? Try it and see for your self.
Now imagine that the blood has transferred to the wrist as Hartley suggests. How does it then begin to separate in to four streams and travel to a point further accross the wrist - and then in a split second, suddenly coagulate and not travel any further?
For a start, I can't put the inside of my wrist against that part of my neck. I can put the lower part of my hand against it though, and yes, I can see how the blood would run. If I'm sitting up, the blood would run towards my elbow, and if I'm lying down, the blood would run towards my fingers, not towards my wrist.