Just to give a heads up I went through several books about Vengeful Teeth.
Not one talked about the spirit not returning to the cycle.
However, IC that is what Brody was taught so he is going to teach the same.
Whether it is true or not, probably could be found out if those doubt Brody's teachings.
There has definitely been RP around it in this game and several others.
It's the sole reason Brody defied Calvin and threw Dimitri into the lake instead of Teeth.
In other words looks like it's not a OOC storyline thing but an IC belief.
OH no Garou are wrong sometimes!