Well, they don't actually state that loading is an exemption, just that they note your reps stating you were unloading. Your case hinges on whether loading/unloading from a vehicle that is not a M/c is an exemption in the m/c parking bay. The Traffic Order is the document that defines what is allowed.
Also, your reps were an informal challenge against the paper PCN, and all London councils game the system ruthlessly and reject virtually all informal reps knowing that most people then just cough-up to get the discount. I call them "Fob Off" letters. So if you are prepared to stand your ground, you must wait for the Notice to Owner, sent to the name and address on the V5C for the vehicle. So, is this your vehicle, and is the V5C Registration Certificate up-to-date ?