If a police officer reasonably believes an offense has been committed. In this case, the offense of disturbing the police, give the police officer the right, under law, to detain you for the purposes of getting your identity.
Now, let's say you don't agree with that (or you don't believe it is reasonable). Then, you have two choices. You can A) comply and make a complaint later. Or B) resist and face charges for resisting (as well as the original offense).
Either choice, you will be lawfully arrested.
If you make the decision to complain. You can bring a charge to court and let the judge decide -- not if you had the right to photograph -- if you could reasonably be said to be disturbing the peace. But, you can't accomplish that without originally complying with the police officer who detains you.
The problem with auditors / sovereign citizens (besides not really knowing the law) is that they believe they can resolve the issue solely by non-compliance. Sometimes, that will work. Sometimes the officer will be busy and their only goal is to get you to stop doing whatever it is you're doing. Just having the right to arrest you doesn't mean a police officer has to (unless you have committed a felony).