The PCN was issued for the wrong contravention.
Clearway parking only applies to the carriageway, not the footways or verges. There is a sign on their rejection showing a ban on parking on these, so the PCN should have been issued for parking off-carriageway, assuming they have created a traffic order for this. The CEO who served the PCN got it wrong, basically. In London, the ban applies from the 70s due to an Act of Parliament, but this was London-specific.
As they haven't re-offered the discount, it is now a no-brainer to take them to the Traffic Penalty Tribunal as the penalty remains the same, and there are no additional costs.