I maintain my point, would we be agreeing with the actions if it was the Governor who killed Carl? Let's say Carl ran straight into him, was surrendering his gun, and the Governor just shot him? Certainly Rick wouldn't agree with the action. I wouldn't agree with it either. Though in saying that I don't agree with it, I do understand Carl's motives. I think he made the wrong choice, but I understand why he made it.
On a similar, but unrelated note, I get the impression from the final moments of the episode that
No,I think leaving an unarmed person to fend for themself with walkers everywhere ,assures death just as a bullet does,its just a slower more passive way to do it.
If anything ,its more cruel than one shot to the head .