Did you reveal the identity of the driver in your appeal? For example, "I did this or that" instead of referring to the driver in the third person: "The driver did this or that"?
As mentioned above, in Scotland there is no Keeper liability (for now). Only the driver can be liable for the charge and the parking operator has no idea of the drivers identity unless the Keeper reveals it, inadvertently or otherwise.
Whilst it is highly unlikely that UK CPM would ever try to make a clam in the Scottish courts under the Simple Procedure, you cannot rule it out 100%. The reason they would not make a claim in Scotland against the driver (assuming they know that the Keeper was also the driver) is because there is no money on it for them even if they were successful. It would cost them more to issue and contest a claim than they could ever hope to recover.
The only reason they still persist in chasing you is because they hope you are low-hanging fruit on the gullible tree that will pay up out of ignorance and fear. As long as you are here receiving advice, you are therefore no longer low-hanging fruit.
If you can, please show us exactly what you put in your appeal. You can safely ignore any debt collector letters they send you (and they will). Debt collector are powerless to do anything except to try and scare the gullible into paying up. The debt collectors are not a party t the contract allegedly breached by the driver. You can safely use their letters as kindling. Ignore them. Never, ever, ever communicate with a useless debt collector.
In all likelyhood, if you just ignore everything you receive about this, 99.9% for sure, nothing will come of it and eventually they will give up.