Agreed on the first part.
It appears that the Terran Empire's rules on this sort of thing are the same as the Klingons (either universe): Anyone can challenge a fellow officer (all the way up to the Captain) to a fight to the death, if they feel that the other is weak or has acted against the interests of the Empire. No "investigation" is necessary, because such challenges/assassinations are legal.
f you win, you move up in rank; if you lose, you die. Everyone knows this going in. That's the end of it, really.
(In the Terran Empire, if you are so bold as to challenge the Captain and win, you apparently don't
become Captain; his/her XO would take command, and everyone else moves up in rank. That's what mu-Chekov said, anyway. Don't know if this is the case with the Klingons.)