In the battle example, they show the active player is the Ultramarine Captain. The Ultramarine Captian has a battle bonus of 2 on any battle. This is not figured in the example.

Ken on Cape said:

I think they didn't mention it because in the example the player had already scored high enough without needing to add the battle bonus

Should have mentioned about the bonus and that it was not being used. Not having it in there at all is not good for the rules.