I think what you've attached is the notice to Keeper, the ntk is the first letter you will receive. Maybe b789 missed it? Don't start thinking about the tricks these companies play, its not helpful, to successfully contest a PCN you need to understand the legal basis for how they operate. Whilst it is not a fine it is an invoice and can be enforced in court as some people unfortunately find out. However it's unlikely to reach that stage and if it does people here will advise you through the process. As for the machine being faulty it's more likely the driver made a mistake either miskeyed the reg and selected the wrong arrival time or paid a long time before they a left the cad park. The payment machine will pick up the entry time from the ANPR camera and calculate how much you owe up to the point of payment. They clearly had the vehicle entry time otherwise there would be no PCN. I'm not ruling out machine error but that will be difficult to prove and if it is driver error they will have a record of when payments were made and the reg entered if it was incorrect.
The NTK looks POFA compliant to me, I'm sure others will check, which legally allows the PPC to transfer liability to the keeper if you don't reveal who was driving. Unfortunately for you the PPC is an IPC member so initial appeal and IAS appeal are likely to be rejected.