....."the basis that it is inequitable to fine someone who is entitled to park there the same amount as someone who is not".....
I suspect it is a public place and therefore anyone can park there as long as they have the required permit or paid parking ticket. Therefore it is not a case of one over another having an entitlement to park there. Are you going to have the same argument over forgetting to tax your car or renewing your driving license or swapping over your insurance disc etc.
Pay the fine and drop it you mad a mistake, learn from it.