Even if he wasn't responsible, I think that Robb Starks death was tactically hurtful to Stannis's cause.
It was. His dumbest move was not setting up a meeting with the North. He never speaks to Rob to find his true intentions. Rob is out there fighting the Lannisters, why would you "want" to kill him? Why would you think the North is a bigger threat to you reclaiming the throne than the grandfather of the king?