I am sorry, but that is not correct. No matter how fast your CPU is processing commands, you will only send and receive so many messages from the server every second. The is what the interpolation settings are for. Since there is lag between computers the interpolation settings guess where you are going to be so that you do not "jump" on other peoples screen. If your computer is faster, you will notice a difference on your screen of how smooth the game is, but no one else will.
By your logic, you're saying that people with better computers run faster in online games than people with old computers. This statement is not true.
As for the OPs issue. I believe that your LERP settings may be off. This means that your computer if interpreting the positions of the other players behind the actual location of their hit box. You could try lowering this in console and seeing if that fixes your issue.
