To be a little pedantic - an FAC proves a legal entitlement to posseess the gun. It doesn't prove you as the legal owner.
I'm not sure if I agree that the cop handled it badly. If the PNC shows the details of all the guns on your cert then yes he did. If not though then what else was he to do? He doesn't know whether you are authorised to possess that particular gun. It may have been one that you had illegally.
J.
but then if he thought the gun was held illeagaly why was,nt i arrested for haveing a unlicensed firearm in my procession ? penalty max 5 years