As a country which lives, rightly or wrongly, under the threat of a sudden invasion to destroy it's "weapons of mass destruction", Iran is quite naturally sensitive to even the suspicion of potential infringment.
Having worked in Aviation in the Arabian Gulf for 20 years, I doubt the authenticity of the exchange. There are a couple of points which stand out in the conversation as being unlikely. I also find it hard to believe that any mature military pilot, would make such a provocative remark in such a sensitive part of the world. I am sure it was intended as a rather poor joke somewhere.
The story has been broadcast very freely over the Internet for some time now.