Actually Constrictors kill by causing Cardiac Arrest in the victim, by causing the veins and arteries in the blood system to become to shallow for blood to flow, thus causing the heart to stop.
Certainly any type of a constriction device: snake, string, or belt can act as a tourniquet and restrict blood flow. However, I think that is more of a collateral action with suffocation still being the primary objective. Blood flow restriction can certainly lead to death, but it would be slower and less efficient then suffocation. I donít doubt you saw this on TV, but I donít think the shows assessment is accurate.