Letter from TNC and aggressive phone call

Ok - so here is my appeal:
You completed the appeal on 03/12/2015 21:39:02.

We are aware of all the signs that alert car park users of the correct use of purchasing and displaying a ticket in the correct manner. However, upon arrival to our vehicle on the 31st July 2015, there was no sign whatsoever of any bright yellow plastic wallet containing a fine issued by a car park attendant on our windscreen, or on any other part of the car. Nor should we have expected to see one as we had purchased and displayed a valid ticket.
Please see attached a scanned copy of the car parking ticket that was purchased and displayed on the driver's side window at the time of purchase, valid within the time in which the parking fine was issued. Whether or not Armtrac can produce evidence that the valid pay and display ticket in question was not clearly displayed on the window remains to be seen, however, that is not the point as we have proved to Armtrac and now to you that we did in fact have a valid ticket. Would it be possible that the parking attendant, the issuer of the PCN, placed the bright yellow plastic wallet over our ticket and not on the windscreen as instructed, subsequently obstructing the view of our valid ticket. Armtrac have already proven themselves to be unscrupulous operators by sending a letter dated 20th October and not posting it out until 4th November; thus leaving us with 6 days to 'pay' or appeal their fine rather than the 21 days we were supposed to have - this has already been brought to your attention and you have investigated it on our behalf, thank you for that.
The original pay and display ticket was sent to Armtrac in response to their initial letter as proof that we did purchase a ticket, though to Armtrac this was not satisfactory evidence.
Please see, the date of issue 31st July 2015, time of issue 13:58, expires 15:58, for use of the car park Stennack Private Pay & Display Car Park, St Ives, Cornwall.
As the operator has claimed to have sent you all the documentation between myself and them, I do not feel it necessary to attach all the letters of communication, but will be happy to if you so desire.

Their Response:
Having considered all of the evidence in this case, I am satisfied that the Operator has established a prima facie case.

The Adjudicators only role is to determine whether the charge is lawful or not. I will only have regard to the legal principles that apply in any matter and NOT to any other feature such as the issues identified with regards to the correspondence between the Operator and Appellant.

The terms and conditions of the contract entered into when parking on the private land in question are clear, a valid pay and display ticket must be displayed.

The photographs of the contravention were taken between 14:50 and 14:52. They show that the only pay and display ticket on display expired at 14:29. It was therefore not a valid ticket.

The photographs also show that the other ticket referred to by the Appellant: date of issue 31st July 2015, time of issue 13:58, expires 15:58 was not on display.

As such the parking charge was validly issued and the appeal dismissed.