Which car park did the driver use at the location? Did anyone in the vehicle have a blue badge and did the driver use a disabled bay? Can you go back and get some photos of the general layout and the signs, in the dark, without using flash or headlights?
Their ANPR images do not show the duration of parking. They simply show the period that the vehicle was on site, which is not parking. There is a minimum 10 minute grace period on top of the paid parking time and they have issued this for allegedly being 1 minute over the grace period.
As this is an NHS Trust facility, who fobbed you off about not being able to get the PCN cancelled. You must email the CEO of the Trust and make a formal complaint.
Also, have you tried the PALS service?