In my perspective it is completely understandable why you killed broken. On another server it might have been a good enough reasoning, however, it's not the case here. I am not a rule fetishist. Your comparison to concentration camps/saudi law is way out of proportion and is unrelated. I didn't say you did the right or wrong thing. You've broken a rule so you got punished for it. In my prior comment I even said that I do not support this rule. If concentration camp workers broke rules they would be punished. If you steal under the saudi law, you will get your hand severed. It doesn't matter if I don't support these laws/rules, the fact remains; you break them, you get punished in one way or another.
Your explanation is that within the seconds Broken killed Grens, you ruled out all possible reasons why he could have done that, you've examined the ground and didn't see any traitor weapons, you've made sure there is no one else inside the cave/no other player has been inside the cave, and based on this you killed Broken. This is simply unrealistic. In another server, I'd probably kill Broken too.
2.1 Random Death Match
Players are not allowed to kill others without a justifiable reason. Random Death Match or RDM is the act of killing without a justifiable/valid reason and is punishable. It is required to ask a player who killed an innocent why they did so, unless you can be certain that they did not have a valid reason. Without a justifiable, or believable reason they can be killed. Read rules 2.6 and 2.7 for more information on when killing people is acceptable.
According to the above and the information you provided, you should've asked.
In addition, it doesn't help that you keep insulting others because of your misdemeanor. Even in-game, after Broken reported you, you weren't warned yet. Only a chat was opened. You being disrespectful towards the users in the chat is not the way to handle things. If you'd explained the situation calmly I doubt you'd end up with 2 warnings. Keeping the insults going even in the forum report only worsen your position. You can disagree with the rule, but while it's there disobeying will result in punishments.