It‘s like pinching a hose. Despite the pressure at the pinch point being higher, distal to the pinchinung the pressure is massively reduced, and only a tricky come out the end of the hose.

Just like you said at the end.

The part you missed is that the injury site itself, keeps the same diameter. To any reduction in diameter proximal to the injury reduces the blood flow. Which reduces the pressure at the site of injury.