I have never heard of any officer refusing to show photo ID. In my (plain clothes) agency, it was the first thing we did unless a gun (and badge) was callled for.
As for "jurisdiction", every state I have lived in (NJ, MASS, NH, CA, AZ), all officers had statewide authority. That is, a Podunk PD officer could, in theory, write a traffic ticket in Big Town. It was not often done, but sometimes .....