You have every right to know and ask what the officer is doing whilst around your car. You have every right to see/know the rules when referring to them. What you needed to do was get a badge number from both officers. People need to get in the habit of asking this. It's in your right to know!
As far as I know, you can't be fined twice for the same offence/defect. Someone feel free to correct me if not the case.
If I were you, I would contest it. Write a letter to the ombudsman, get legal advice if you have to. What they've done sounds very unjust and should be taken further. I wouldn't pay a cent before getting legal advice. Don't think you could contest the defect, that sounds legitimate, unfortunately. But the fines are another matter.
Best of luck mate.