Also remember the Klingons asking Kirk if he's willing to give up starfleet. I guess everybody is enjoying the same strawman, right ?
As a matter of fact, they are.
Because I also
remember Valeris quoting Kirk's words at the end of that very same briefing: "Did you not wish Gorkon dead? 'Let them die,' you said. Did I misinterpret you?"
Cartwright's co-conspirators were listening in on that conversation, either a recording or in real time. Chang brought it up in the first place as a way of baiting Kirk into saying something undiplomatic. He nearly succeeded.
If Starfleet isn't the Federation military, then who is?