Strictly, yes. We are a part of the system, no matter how much you may want to believe otherwise.
Further, murder is an action of man, and therefore natural under your definition - does that mean it should be permissible?
When a soldier kills an enemy soldier, is that murder?
How do you derive a moral code by which to live? I will try and conform my arguments to that rationale, if possible.
That "moral code" would be a system of behaviors approved / disapproved based on how it supports a social system that is vital if Man is to maximize his chances of survival on this wild planet; and his rights, as an individual. We struck a balance, a long time ago, that resulted in every viable society shunning murder, because it is detrimental to the coherence of any social grouping, thus endangering the viability of each entity in that grouping if the society were to break down.
Okay. Utilitarian, but legitimate. Now, the money questions - how do you define Man? And how do you delineate "rights"?