Many people have set and watched them only to go, "WTF that is not what happened!" Well hopefully I can answer that to a few people on why it will do that at times. The truth is that CoD does not have kill cams, it has a death cam, and they are two very separate things in how they work and what they show. Even the final kill cam of a match is not a true kill cam it is still a death cam.
Kill cams show from the killing players view of how they killed the player. Normally you would be seeing through their eyes as you came around the corner and they fired upon you. The same as how in skyrim or fallout it shows you killing the enemy when it does the slow motion replay of the kill even up to following the arrow/bullet as it travels and hits and kills them. In CoD however what you see if from your perspective of how you came around the corner and seen them and then died. Which is what a death cam does.
The thing about death cams is they only show the action a second or two before the death and up to the death not afterwards, everything you see on your screen does not matter for what it is really showing is the action from the killers side of the story but letting you see it through your eyes instead. Making what is seen often out of sync and backwards from what you remember happening.
ie; player A comes around the corner spots player B. He takes aim and fire's several rounds and yet dies. He watches the kill cam and it never shows him firing at all. Player B on the other hand seen the player come around the corner fired several rounds too. Because of his closer connection to the host having less ping/latency because of distance his shots on his console registered a split second sooner and was time stamped a split second sooner and sent to the host. The host getting the data from player A compares to what player B sent, which was a split second sooner and decided that Player B got the kill and then sent the kill flag out to player A. Everything that Player A did after the host sent the flag but has not yet received it means nothing at that point. YOU are dead and just have not been told so yet. You can run, jump and drop shot but you are dead. That split second later you die even having moved from where you were.
This is and always will be the true nature of the beast when playing online in a fast paced game like a fps where even .00001 seconds mean life or death. Not what you seen with your naked eyes, but the time stamp the computer see's on the packets.
Now the replay data is sent for the kill cam. It never shows you firing but maybe one round. Because the host checked the data from B and the time stamp said you were dead already before you fired more than that one round, so it discarded all the animation of you shooting at them in the replay packet. So your console gets the replay information and renders it, but does not show you firing for it only counted up to the moment you were already considered dead by the other player and host. So all you see is your one shot fired, and their entire stream of rounds and you dieing.
Which is why most people say never believe the kill cam for it is never 100% accurate to what you seen on your screen and most times will not ever be unless both players are equal distance from the host and have comparable connections and ping to the host. For really it is showing you how the killer reported to the host of what they seen and of how you died and not what you seen or remembered happening just rendered in your view instead of theirs.