you are in fact correct, but of course the police will never admit to this if they can get away with it.
If you are beyond the 5 year point with a SHPO active, you are entitled to apply to the courts (with out permission from the police) to potentially have it discharged in full. If a SHPO is discharged the conviction would be considered as spent, regardless if you remained on the SOR.
In order for a discharge, you must provide evidence to state why you believe the SHPO must be discharged, the main thing the courts will consider first is. Changes in your circumstances (obtaining work, making new friends, new relationships, steps taken to keep you from re-offending), issues in which the SHPO prevents you from a change in circumstance (if the SHPO is preventing you from working and you can prove it, this will go in you're favor)
If you are considering taking this step, contact various solicitors and see if they allow legal aid to represent you. Not all solicitors will do this, but some might if you ask. This would mean you get free legal advice to proceed with your application. Other wise you would have to represent your self in court.
I applied to have my SHPO discharged 2 years ago, I finally managed it Feb last year after many hearings due to the police failing to show. I was successful because I proved because of my SHPO, it was hindering my ability to not only seek out work, but relevant training to help aid me in to work also. Therefor, the SHPO it's self was preventing me from changing my circumstances.
It is highly suggested for the best outcome, that police get on board to allow the discharge to happen, but considering the officer told you what you said was not true, It is very unlikely you will get their support in this. However, you could always talk to his superior if you wish.
As for DBS checks, You are correct and I believe a basic will not show your convictions that are considered spent, but higher checks will list both unspent and spent convictions.