Say Mr. X is pointing his gun and trying to kill me. My friend, happened to be walking by, grabs Mr. X and struggles to tackle him to the ground. I tell my friend, "No, go away; I got him!"
I have my gun, I shoot Mr. X; the bullet goes through his body and kills my friend too.
The Torah's story about an accidental death talks about a more direct death - I was chopping a tree and the handle flew off and killed someone who was passing by.
In this situation, my friend was trying to help me, and, was aware of the dangers in doing so, as he saw the man with the gun, and he heard me warn him to go away. In a sense, it wasn't a direct "accident" as described in the Torah, from what I can tell. My friend, "volunteered" to help and place himself in danger.
Given this scenario, is this considered a type of accidental death that would require me to go to a refuge city?