Sirius' death is a consequence of his own action, surely, not Harry's. Harry may have been the catalyst, but Sirius knew that he was not supposed to leave the house.

I'm going a bit OT here, but I think it's fair to say that Sirius died because he was protecting Harry and his friends, the fact that he was supposed to stay at Grimmauld Place was quite irrelevant. Any of those who went after the children might just as easily have been killed.