Maybe the losing team got a kill before your team confirmed the tag to make your kill featured in the GWK and for some reason it didn't count because of that.

That said, I have gotten a lot of weird and inaccurate GWK achievements or whatever in my MW3 career so it wouldn't be surprising if the game also failed to properly award an GWK achievement from time to time.  That would really suck to lose that one though since it's pretty frickin' hard to get.

not sure if its just wonky or if there are stipulations but yes kill confirmed kill cams sometimes give you the challenges sometimes dont.  I too have gotten killcam titles and emblems in one game without doing the challenge itself and in one instance without even getting the killcam, so who knows.

KC is a bit of an oddity when it comes to the GW kill challenges, They do count but there are some exceptions. I found that the ones that counted for me were gw kills where I killed the person and picked up the tag to confirm the final point. Which made it easy for the challenge get 20 game winning kills. However when it comes to kill streak kills like AC130, airstrike, care package etc it made it more difficult as you could not always be around to confirm the kill.

Without seeing the video my guess would be either the other team got a kill after the care pack or someone picked up another tag for the win thus negating the challenge. The best and most consistant game modes to complete the challenges are TDM and FFA.