Yes you are quite correct. But usually the owner of the car is who the penalty is against, if they are the primary user, whether they are the registered keeper or not. With this in mind it shouldn’t affect the registered keeper, until they are penalised for the owners actions then it is for the registered keeper to prove they are not the owner, so they consequences go towards the owner.
The reason they take the car is because the car will be registered against a name and address (the registered keeper) the DVLA do not record the owner, therefore when that car has been in contravention of something, they will know where it is located and seize it based on court orders.
I understand what you mean about fairness, however it is the vehicle which has been used to commit an offence and they are entitled to do so based on the law. It will then be between the registered keeper and the owner to establish who will be liable for the fines incurred. It will be assumed it is the registered keeper unless proven otherwise.
For it to get to the stage of bailiffs, especially for a parking ticket, it means judgment has been enforced so the registered keeper must have been ignoring court documents which is not looked upon favourably and payments for a fine has not been made. This could have been avoided.
Data Protection exemptions come into it because they cannot use the personal details for any other reason than to locate the vehicle for the purposes of enforcement of a court order.
I am unsure if you are the registered keeper or the owner but payment will need to be made to get the vehicle back, either by the owner or the registered keeper; ideally for the person who incurred the fine and debt. The court order would have given 21 days to pay the original charge and if no response that is when bailiffs are instructed.
You could have made an “out of time challenge” but you would need good reasons for doing so. But again, there are time limits to doing this. From what you have stated, it is too late, and the debt will now need to be paid or the car can be sold.