Been using the Ballista and trying to get it gold. Once I hit 6 Bloodthirsty medals it just stopped there. since then I have got 3 using nothing but the Ballista in games of Search and Destroy and Domination. So I've had 9 Bloodthirsties but it seems to think I've only had 6. You owe me a gold Ballista Treyarch! (In one Bloodthirsty's time respectively)
They don't count towards the challenge if you get them across multiple rounds. Considering you mentioned SnD most likely that is why you didn't get them. The same thing happens in DOM if you get it across the rounds.
I thought of this but the exact same thing happened when I was getting my executioner gold. Kept hitting bloodthirsties but I ended up having to do about 15. And this was in Kill Confirmed! And to avoid confusion I never equip a secondary or a lethal (Excluding a tomahawk for spawning, jumping and hurling) So I know for sure all kills came from the weapon of focus. :/
Perhaps your scorestreak selection is doing you in. If you get a kill with any of them before you get the Bloodthirsty it will also not count. I always make sure to only run one and done streaks and I save them until after I get my Bloodthirsty or I run non-lethal streaks.
Only ever run UAV, VSAT and something higher and the VSAT isn't even achieved until at least a bloodthirsty in most cases (Unless you're a dogtag-stealing-sodomite)