You can dispense with 'the driver' if it's you. This is owner liability and if you were the driver then your evidence is first-hand and any reps submitted would carry more conviction.
If you are not the owner (registered keeper) then I'd keep them in the loop.
A 30-minute bay suggests high turnover and that it's likely to be enforced. As stated, there's no 'grace' period of 10 minutes in Wales and as far as the evidence is concerned and irrespective of when you parked 14.37-15.08 is more than 30 minutes.
As suggested, asking them to accept that the contravention was de minimis and that they should exercise discretion would seem to be your best bet. Don't risk antagonising them by reference to valve positions unless you know the vehicle was not parked as alleged, in which case it's 'contravention did not occur' but you'd need evidence.