It is unfair but you are dealing with a firm of ex-clamper thugs who are out to scam you. This is easily defenced, however, any initial appeal and subsequent secondary appeal is not going to work.
PCM are an IPC member and their trade association are simply a cartel whose only interest is protecting their members. Their secondary, supposedly "independent" appeals service, is simply a kangaroo court and less than 5% of appeals submitted are accepted.
Not to worry though. There are 4 plans of action. Plan A is to get the landowner or whoever contracted PCM to get the PCN cancelled. Find out if it is the Co Op who either own the land or contracted PCM to manage the car park. If so, email the CEO or as high up the management food chain you can go and explain that as a patron of their store, you do not expect to be invoiced by an unregulated private parking company for £100.
Plan B is to appeal to PCM, for what it's worth. However, there is a flaw in their Notice to Keeper (NtK) which renders it non-compliant with The Protection of Freedoms Act 2012 (PoFA). What this means is that if they do not know the identity of the driver, they cannot transfer liability to the keeper. So, any appeal is made by the keeper and, as there is no legal obligation to identify the driver to an unregulated private parking company, you decline to do so.
The keeper will need to make sure that they do not identify the driver inadvertently or otherwise. If selecting any options, do not select "driver". Only "keeper" or "other".
As the Plan B appeal will be rejected, there is then Plan C. Personally, I wouldn't bother but others on here would suggest that a less than 5% chance of convincing a cabal of incestuous paralegals that they should deny their paymasters their scam money, is still worthwhile.
Which leads on to Plan D, the ultimate dispute resolution service, the small claims track in the County Court where the only truly independent arbiter, a judge, would decide whether you owe PCM a debt. This is the most likely outcome but it is rare that it would actually get to a hearing as most of these claims are discontinued.
The keeper would receive a whole load of debt collector letters before this stage but they can ll be safely ignored as the debt collectors have no powers as they are third party to the contract the driver is alleged to ahem breached. This process is solely aimed at getting the low-hanging fruit on the gullible tree to capitulate and pay up. They rely on the ignorance of the majority of their victims on how the civil litigation process works. If you are here getting advice, you will not be low-hanging fruit.
There is a very small (minuscule) risk that a defence to a claim is not accepted by the judge, in which case they would find against the defendant and a CCJ is issued. However, there is no danger of a CCJ being on your credit record as long as it is paid in full within 28 days of judgment. If paid in full within that period, the CCJ is expunged from the record as though it never existed. As this would be a "small" claim, costs are fixed and any fake add ons already claimed by the useless debt collectors are not allowed. In the very worst case scenario where a claim was unsuccessfully defended, it would be no more than the £100 PCN charge plus a £35 court fee and £50 fixed legal costs. However, as I have said, that is an extremely remote likelihood.
The normal modus operandi of these scammers is to try and scare you into paying with useless threats of litigation and then filing a claim through one of the roboclaim firms of bottom-dwelling solicitors and going all the way up to the date they have to file their trial fee and if the defendant hasn't capitulated by then, they discontinue and move on to lower-hanging fruit.
We also have a very good defence which is likely to lead to a claim either being struck-out or discontinued before it ever gets to a hearing. The latest defence strategy having been advised by a long serving district judge who knows how these abusers of the court system operate.
So, for now, you need to try Plan A. Any Plan B appeal, for what it's worth, can be made just before the 28 day deadline. Just remember, do not identify the driver. The keeper is doing all the work and simply says things like "The driver did this or that...". No "I did this or that...".