Actually cross referencing ANPR data with VRMs entered is quite a big thing to implement and comes with some major downsides (not withstanding loss of revenue). It can cause more problems than it solves, people get quite upset when the system rejects their VRM, quite often because the cameras have failed to pick up the vehicle entry not to mention people not knowing the difference between 0 and O.
Checking the ANPR logs when your know what you're looking for is simple but doing that automatically looking for every permutation of incorrectly entered VRM is not. Hence why it's worth appealing, gives the parking company and opportunity to cancel the PCN, obviously if they will very much depends on the operator, which trade body their are a member of can be a good indication of how they approach things.
The requirements for manually checking the ANPR data does not extend to cross checking permits etc. and it wouldn't be practical to do so. Having worked in a number of industries where manual checking of things is performed I'd rather have an automated system do it any day of the week rather than someone on a target being paid minimum wage who doesn't care. Even engaged, intelligent people switch off pretty quickly and miss things.
