He thinks the wording of "enemy creature" refers to the creatures enemy not the controller of nullify's enemy.
It doesn't mention "enemy creature" though. What it mentions is "an incantation or enchantment controlled by an opponent" I agree that this wording may be slightly ambiguous, but I assure you that it means an opponent of the controller of the Nullify spell and not of the creature that it is attached to.
It may help to always consider a spell to be talking directly to it's own controller. Then, any ambiguity can be resolved by assuming it is referring to it's own controller. Vague references of friendly or opponent tends to mean friendly to it's own controller or an opponent of it's own controller. If it was trying to make a different reference, it would typically make an effort to clarify it, such as by saying "an opponent of the creature." If there is no specific clarification, it should be safe to assume it is referencing you, it's controller.