I joined the Dark Brotherhood and noticed something strange while doing assassination missions. When I have an quest active to kill so-and-so, they do not respond to the world around them. As an example, I had to kill a guy and I was next to him and invisible. Then a dragon came around and started attacking me. The target did not react to the dragon being there at all. To make matters worse, he didn't seem to even take any damage from it.
I attempted to have the dragon kill the guy for me by drinking a fire res potion, then position the guy between me and the dragon. The dude just stood there like nothing was going on when the dragon breathed fire on him to get to me.
Is this normal or maybe some bug due to the quest?