Is it the case that the vehicle hirer in the current case is the same person or entity to whom liability was recently transferred for PCNs CU67189608 & CU67327869?
For that matter is the same vehicle involved?
As I understand you the hire company maintains two discrete hire agreements in respect of any given hire of one of your vehicles? Upon receipt of a PCN one or the other agrrement will be sent with representations to the Enforcement Authority depending on the legislation that the PCN is issued under? The hire agreements will have differing rental periods?
However the bottom line is that you, the hirer, have a Notice of Rejection in respect of a PCN that the hire company received. This should be a London Locsl Authorities and Transport for London PCN.
The options on the table are pay-up or appeal to the Adjudicator. The Adjudicator can decide if the Hire Agreement that you provided to Camden is valid or not. You'll be in for the £130 penalty if you lose.
I would register an appeal. State that you rely on your representations and that further evidence may follow. Ask for a personal hearing, you can vary this to a telephone hearing later. Use the time to research the status of the hire agreements.