In order to assist the OP in undertaking the nuances, the "driver" and the "keeper"/"hirer" are separate legal entities. When it comes to PCNs issued by unregulated private parking companies, it is the unknown driver who is liable for any alleged breach of contract between them and the PPC.
In this case, as the driver is unknown the PPC requests the keepers data from the DVLA. The keeper is known and as the vehicle is leased or hired, the known keeper transfers liability from themselves to the hirer who is also known.
At this stage, the driver is still unknown. The only way the driver can become known is if the known hirer tells the PPC, inadvertently or otherwise. The PPC cannot infer or assume the known hirer is also the unknown driver.
The only way that the PPC can transfer liability for the PCN from the unknown driver to the known hirer is if they fully comply with all the requirements of PoFA. They haven't.
Because the PPC has not fully complied with the requirements of PoFA, only the unknown driver is liable for the PCN. As there is no legal obligation for the known keeper to name the unknown driver, the PPC will have no way of progressing with collecting the alleged debt.
The burden of proof is on the PPC to show that the known keeper was also the unknown driver. How do you think they can do that unless the known keeper tells them, inadvertently or otherwise?
So, without even looking at the notices (speculative invoices) you received, because you have told us that the vehicle is hired/leased, together with our knowledge that in 99.999% of PCNs issued to hired/leased vehicles, the PPC will fail to follow the correct procedures as required in PoFA paragraphs 13 and 14.
The PCN is for £100 with a £40 bribe discount designed to get the gullible to pay up without forcing the PPC to have to deal with appeals . They live in the hope that out of the 40,000 PCNs issued by unregulated private parking companies EVRY DAY, most victims either do owe them a debt or are ignorant enough to fall for what they think is a "fine" when, in fact, it is nothing of the sort.