If you've been downing enemies, not receiving the kill, and wondering why, we can confirm that it is not a bug. Currently, the way the game is programmed, it's players who finish enemies off that are awarded the kill.
This has of course caused a lot of confusion and frustration in the community, with most people (rightly, we think) claiming that whoever downs an enemy should be awarded with the kill, not whoever happens to finish them off.
The policy has had other unwanted effects too, like incentivising your team-mates to stick back and wait for you to do most of the work (and also see whether you survive) and then come in afterwards to finish anyone off.
The good news, though, is that all this is about to change! Infinity Ward director Joe Cecot tweeted earlier today that "In the next title update (larger update) the person who downed will get the kill credit. The change just missed release."
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In the next title update (larger update) the person who downed will get the kill credit. The change just missed release.
— Joe Cecot (@JoeCecot) March 12, 2020
The only question remaining is when exactly will this change be rolled out. If it's part of a much larger one, we can't wait to see what other balance and meta altering adjustments are going to be made!