My view is slightly different - if you have a meritoious defence (ie that the driver read the terms, sought to pay, couldn't and therefore left to park elsewhere), then there's certainly no harm in pointing this out to the parking company.
If you do, show us what you plan to send before appealing, and appeal only as the registered keeper, giving no hint as to who was driving.
They'll reject of course, but if they then go on to issue a court claim it can be painted as rather unreasonable (alongside other available defences).