Not necessarily unilaterally, no.
The parking company may have an agreement with them allowing them to cancel X% of PCNs only.
The parking company’s contract usually is that the money for parking is passed to the land owner, with the appropriate VAT implication, but that the parking company’s contract means they can usually pursue anyone who doesn’t pay or otherwise breaks the rules, and the parking company can keep all the money it obtains this way. This is the sole or main income stream for the parking company, and they won’t want to fetter it with a right for the land owner to deprive them of it. Ultimately the land owner can terminate the contract, so the parking company will take away its equipment and leave the land owner in the position they were when they engaged them.
The industry issues something like 40,000 PCNs daily, and if only 25% of them are paid it’s a net flow of £1m/day to these companies. They want to hang on to all of this.