"I shot the one closest to me" is a statement of fact, not motivation. "Just" is an indicator of temporal proximity, not thought processes.
I can see temporal proximity as an explanation, just not a very good one. If "just" is, indeed an indicator of temporal proximity, it could be replaced with a synonym and still make sense.
"Moments ago, I shot the one next to me."
"Right before I made this statement, I shot the one next to me."
"Previously, I shot the one next to me."
All are different indicators of temporal proximity synonymous with "just", and although they do form complete sentences, they don't have the same coherence as if we replaced the synonym for "just" meaning temporal proximity with a synonym for "just" meaning thought processes.
"I up and shot the one next to me."
"Out of the blue, I shot the one next to me."
"After making a random selection, I shot the one next to me."
I believe the statement that he "just shot the one next to him", is more an indicator of thought processes answering the question of
why and how he decided which person to shoot than a statement of
when he performed the action of shooting.
However, this is a very vague arguement. Kind of like arguing what the definition of "is" is.
"I just bought a new car." is most likely an indicator of temporal proximity.
"I just bought the damned thing." is most likely an indicator of thought processes.
Similarly, "I just shot a man who threatened me" is different than, "I just shot the one next to me".
It's really fuzzy, but the difference is there.
Of course, that's the strange thing about analyzing the actions and statements of people. We'll never know the absolute truth. We'll simply have to form our own opinions of it.