So the problem here is basically that he's James T. Kirk.
Or are you seriously going to tell me that Kirk never broke the rules.
As for the lying in a report thing, didn't Janeway once make it sound like Kirk had a habit of fudging the details in his reports.
Well the confusion of reality and fiction is one problem of these films. "He is James T. Kirk, he just HAS to be Captain of the Enterprise."
So basically your problem boils down to them doing something that isn't realistic aka business as usual in a Star Trek production.
I mean they had a fraking magic torpedo that made planets for God's sake.
And your telling me Kirk getting a three-step promotion from lieutenant to captain for saving the capital of the federation from a mad terrorist with a WMD never mind stopping him from taking out the rest of the federation breaks your suspension of disbelief
And the main reason for this is that he acts like SLIGHTLY more of a jerk than usual.
Franchise demands put over logical character development.
When the frak has Star Trek ever had logical character development?