You are overthinking it. I you want to continue to do so, then please study the PPSCoP first and then come up with better thoughts!
BPA/IPC Private Parking Single Code of Practice (PPSCoP)Annex B is the section that applies with reference to section 5.1 and 5.2.
Suffice it to say that the PCN is nothing more than a speculative invoice for an alleged breach of contract by the driver. The operative word is "contract". A contract by conduct cannot be entered into unless the driver has had an opportunity to consider the terms and conditions of that contract.
The PPSCoP requires the operator to allow a minimum consideration period before deciding to either accept this e terms and park or leave. The minimum consideration period is 5 minutes (it may be longer). Unless the operator can evidence that a contract was entered into, which can only be done if they can evidence that the vehicle was parked for longer than that minimum consideration period, then they cannot prove that a contract was ever entered into in the first place.
So, the Keeper received an invoice because they allege that the driver breached the contractual terms and conditions. There is no evidence that the driver did so, therefore the invoice (the PCN) is invalid.
Do you still want to argue the point?
Check the appeal rejection letter. The POPLA reference number should be in the header at the top of the letter.