Nagato fucks with and resets reality too. Is she god?
Also, she has no control over distortions personally, nor any knowledge of them. For all we know, an outside influence is doing all of the resets and alterations concerning Haruhi.
Nevertheless, only the Espers mention the possibility that she could be God, and this is because they choose to rule out no possibilities, including that the universe was created 5 minutes ago. Everything Koizumi suggests is pure speculation. And he's full of shit.