... Having said that, though, I've always believed Peter intended to kill Norman in Revelations, when he threw a bag full of Pumpkin Bombs at him. Not something that Peter would've done in a more rational state -- but he'd just seen Ben get glider'd and melt in front him and Norman was heavily implying he'd either killed or kidnapped the baby.
So, yeah. Peter Parker's not a hero because he doesn't have it in him to kill. He's a hero because he could pushed that far, but refuses to give in.