The site management would say that. However, if they are the party that contracted PCS, then they are jointly and severally liable for the actions of their agent.
For now, the Keeper should not do anything. If PCS apply to the DVLA without being accredited to the IPC, then they are acting unlawfully and breaching the keepers GDPR. You can guarantee that without accreditation, their contractual right to even issue PCNs is invalid.
They are not permitted to request DVLA data under PoFA before 4th June, so don’t expect anything from them before 7th-8th June, assuming they try to breach the KADOE contract and then lose their access permanently.