CPL instructors make mistakes. OC in general is legal in Michigan. When it comes to ID, if you are on foot (not operating a vehicle), and not in a PFZ then ID is NOT required. If you are in a PFZ, then it becomes debatable. Some say that you have to prove you have a CPL when OCing in a PFZ, others say not. There have been no test cases on this so it's still up to the courts to decide.
My personal advice is that if you OC in a PFZ and an officer demands ID, give it unless you have the desire and money to be a test case. Again that is just my two cents.