Please clarify: "The owner of my vehicle has received a PCN". The "owner" is not a term that is used in these matters. The "owner" can be anyone, anywhere.
What is important, is to know who is the Registered Keeper (RK). It is the RK who has received the postal Notice to Keeper (NtK). It is the Driver who is liable. The RK and the Driver are two separate legal entities. Whilst the Driver is always liable, the RK may pr may not be.
The unregulated private parking company does not know the identity of the Driver. The RK is under no legal obligation to identify the driver. The RK can only be liable if they admit to also being the Driver, inadvertently or otherwise, or the RK can also be liable if the Parking Charge Notice (PCN) is fully compliant with all the requirements of PoFA.
So, the PCN has been issued as a postal NtK to the RK. So, what is your status in the matter which needs clarifying before advice can be given. Are you the "owner" and meant to say the RK and the Driver was someone else?