So just to clarify - at the time of me entering the CAZ, the car would have been showing as non-compliant on the CAZ website checker.
I did not know there was such a website and I assumed that as my car was ULEZ compliant, it would also have been CAZ compliant.
The "miracle" which had happened was me obtaining the relevant documents proving my car was compliant and getting the CAZ admin team (who were very helpful btw) to update their database.
Birmingham council then checked the latest database and dropped the charges. I doubt they have the tech know how to get a backdated version of the CAZ database