Sorry I am away for a few days and don’t have access to all of this, is it possible to get some general advice?
How long is "a few days" ?
Their rejection letter is in response to an informal challenge, and will not doubt tell you if you want to take the matter further, to wait for the Notice to Owner, Are you the owner, with your name and address on the V5 Registration Certificate ?
Apart from answers to the above, no more meaningful advice can be given without sight of the documents.
If you give us car reg number and PCN number, we can look to see what evidence they have.