I was under the impression that, as records officer and the only other person besides the captain and Spock to have that capability with the ship's computer, Finney could put his name at the top of the list when it suited him.
I guess so. I mean, I doubt anybody would remember what that list looked like if ion storms were only rarely encountered.
That would definitely cinch this as a carefully preplanned crime, then, and not a spur-of-the-moment action that Finney then perfected by "posthumously" faking the visual records of Kirk's finger movements during his "demise". The former makes so much more sense anyway.