Is there more than one car park at the location or is the car park split and operated by two different companies? It is sometimes the case that these scammers will share a location and have two sets of payment machines for each separate area of the car park and it is easy for a driver to make a payment to the wrong operator.
As you can see below, the post code provided in the NtK covers a very small area and there are several car parks next to it:
If you are sure that the driver paid for the correct car park then the keeper should appeal on the evidence and also that the NtK does not fully comply with all the requirements of PoFA to be able to hold the keeper liable as there is no "invitation", nor any synonym of the word, for the keeper to pay the charge.
Do you have or can you get any photos of the signs at the location?
Your friend has never been "fined" by an unregulated private parking company. What has been received by the keeper is simply a speculative invoice. A PPC is not an "authority" of any kind and cannot issue "fines" or "penalties" and no "offence" has been committed by the driver.