Entirely possible that this simply glitched up for you. As soon as I found a "mounted gun", I used it to obtain my 10 kills before moving on. I only had the first set of tatoo's unlocked at that point and was simply trying to do as much as possible before I moved further into the game.
I got my Pistol kills at the same time.
I suggest you perhaps create a second save and see if you can obtain the kills in a new file? If you can, then it's likely your first file is simply glitched. There have been a lot of reported glitches to do with the skill tree from what I've read.
"It's worth remembering that all reviews are subjective personal opinions and if you personally enjoy the game, then they shouldn't get to you. Unless there's a dispicable nagging little doubt in the back of your mind that maybe you're not having as much fun as you've convinced yourself you're having. And won't go away no matter how many times you try to slap it away with weak excuses."