As you can see here the game uses the time sent with the event from the client if antilag or lag compensation is enabled. If its turned off it will use the local time of the server. Which is why for example in extreme cases you can die after getting behind cover and in the kill cam you did not make it there by far.

On BO2 retail (BO2 dedicated servers actually do have that dvar and its functional) g_antilag is non existant it will always use the time sent by the client, aka antilag is always on.

lag compensation

lag compensation? What does that do and how do you remove it. I never knew about this.

I yeeted out lag compensation out of IW5 and T6 on my servers. Works pretty well if you have a stable internet connection, frames and non retarded network configs.