A couple of things are at play when you interrupt blood flow to the brain. Blood flows into the brain by two sets of separate carotid arteries, the internals, and the externals; that is 4 arteries. Two other major arteries that supply blood are the vertebral arteries. All of the blood flow enters what is known as the Circle Of Willis. The Circle of Willis distributes blood to the brain. The "Jugulars" that you say get pinched off, do indeed get occluded, but they are veins and drain the head of blood, they do not supply blood to the brain. When you choke someone, there is still blood flow to the brain, so something else is going on as well.
With increased pressure on the external carotid arteries, the pressure skyrockets inside the blood vessels There are Carotid Bodies which monitor beat to beat pressure within the arteries. There is a reflex known as the "Herring Breuer" reflex that interprets this increased pressure as harmful to the brain. In response, the heart rate slows dramatically and other blood vessels in the body dilate in an emergency measure to save the brain from an overpressure event. Someone who is at the fitness level of a Special Forces Soldier probably has a resting pulse rate well below 60, probably ten to twenty beats lower per minute. So you take this already slow heart rate and it gets driven even lower. It is a clinically significant slowing of the heart rate. So there is more going on than a simple reduction of blood flow to the brain, there are severe cardio-vascular results as well. A good part of what happens with these "Blood Chokes" is cardiac and other measures to lower the blood pressure within the body. I do not know if the airway was damaged causing lack of air to the lungs, it is a possibility.
We'll see what the investigation shows, but it is for sure he was murdered and asphyxiation was the call. The brain did not get the blood and oxygen flow it needed to stay alive. You are a Navy Corpsman and when you hand out medical advice or information, it better be dead on accurate. Check your anatomy again regarding the "Jugulars".
ETA. I do hope you are not playing any of these games.