I strongly suspect there are exceptions to this rule. At the very least we know there exist people in prisons today who enjoy murder. Arguably that's very different since (I assume) 'enjoying killing' and 'enjoying getting shot back at' are worlds apart. But, would it surprise you if there was a small minority of drone operators who genuinely enjoyed their work?
Then again I suppose (hope) the modern military system might select against that kind of mindset.
I don't mean any offense by this, I'm trying to say it delicately, but I think "anybody who brags about killing in combat is lying" is something of 'white lie', probably earnestly believed by most who repeat it, meant to preserve the reputation of combat veterans as a whole by discrediting any veteran who would be so tactless as to brag about killing. I believe it's basically a way of credibly stating "this person who's making the rest of us look bad by association does not represent us."
There's another musician I know in that scene (but in a different part of the US) who was in Vietnam. No one could ever get him to talk about his combat experience. There was one time that we succeeded on steering him onto the topic, and we very soon changed the subject and stopped bringing it up. (He was also one of the nicest guys I ever met, unless he was being blunt about music. He also could play Santa Claus without a disguise!)
Do you think Timothy McVeigh ever fabricated enjoying killing? There are accounts from his fellow soldiers that he quite enjoyed shooting at enemies. My estimation, from life experience, is that there are definitely sociopaths and psychopaths out there. 99%+ of people aren't like that, but you will definitely meet them all the same.
We shouldn't simplify reality just to paint pretty pictures for ideological reasons. Life is messy and there is a nasty side to reality. Hopefully, we won't have to deal with it that often.
I met this fellow musician at a jam session in St. Paul. Somehow the conversation got around to the military, and he proudly said he was the 3rd generation of men in his family who had signed up for the Marines. He bragged that it was the way the men in his family got to kill people. As in, they enjoyed it, and that was the legal and moral way to do it. It's not like the family was poor and had to do it, either. He was a...fellow who could cause consternation. However, he was quite likable in a way as well.
I'm glad that such people exist and manage to lead law abiding, productive lives.