Lag compensation
The server rewinds the world to the instant the shooter actually saw, so hits register despite network latency.
In an authoritative shooter the server decides who got hit, but each client sees the world 50–150 ms in the past. Lag compensation stores a short history of every player's position, and when a shot arrives it rewinds everyone to the moment the shooter really saw before testing the hit. Yahn Bernier described the technique for Valve's engine around 2001 (Counter-Strike).
It's why your aim feels honest — and also why you sometimes "die behind a wall": you were still exposed on the shooter's slightly older screen when the shot landed.