I had to refresh myself on the law... when I first watched the video, I thought he was in violation of the law for not providing his name (I knew you didn't have to provide a physical ID, but I thought name was required). After reading up on Arizona's "stop and identify" statute, however (ARS 13-2412), I found that I was incorrect and he was well within the law by refusing to ID himself.
The text of the statute:
Good for him - I hope I do as well if the situation ever arises, although as he noted... it's quite a rarity in AZ.13-2412. Refusing to provide truthful name when lawfully detained; classification
A. It is unlawful for a person, after being advised that the person's refusal to answer is unlawful, to fail or refuse to state the person's true full name on request of a peace officer who has lawfully detained the person based on reasonable suspicion that the person has committed, is committing or is about to commit a crime. A person detained under this section shall state the person's true full name, but shall not be compelled to answer any other inquiry of a peace officer.
B. A person who violates this section is guilty of a class 2 misdemeanor.