@RockDokRockBecause you are experiencing their lag, not them. You and them are playing the game on different consoles/PCs, and the information is being passed to the server between each. The lag is their information being uploaded. Upload speeds are about a quarter of download speeds.
The server is constantly getting out-of-sync information from their console and it is trying desperately to correct that data before it is passed to your console. As a result, their position is being updated in a staccato nature on your console, instead of smooth as normal.
On their console, your position and gameplay is being reported accurately and they are reacting to it, hence they can shoot you without being bothered by the lag. It's their 'uploading lag' that is giving you the disadvantage.