In today's society, nuclear weapons should be a deterrent, but no one can confirm or deny it.

The difference between true and false is not significant; Iran can shout to its own people that they have nuclear weapons, but the international community says they do not and knows they do not. Even if Iran continues to shout that they actually do have them, no one can disprove it.

It's just like laundry detergent; it won't be proven until they actually use it.