You know how this would work in real life: having done exactly the right thing, the thing that had to be done, Kirk would be put on trial for murder.
"Why did you decide to follow Mr. Mitchell?"
Anyway, I'm glad things went down the way they did. A Shatner-Kirk fistfight is better, more stylish, than what you typically got on other action shows. Add in some Star Trek fight music, which is also superior, and its pure action heaven.