I haven’t heard of “Pay My Fuel” (PMF). However there have been a number of threads on another forum with similar topics involving a firm of solicitors called QDR. They operate on a similar model.
Their letters do not mention an intended prosecution nor do they mention a penalty charge.
There were different opinions in responses to those threads. The principal issue that I could see was that QDR make their demand solely on the basis that the person they demand payment from is the Registered Keeper. It seems “Pay My Fuel” do the same. That’s not surprising as they have no idea who was actually responsible for the alleged debt.
QDR have no interest in pursuing anybody other than the RK. In one thread the RK was not in the car at the time and he offered to provide the driver’s details to QDR. They didn’t want to know. In another the debt arose because of a fault with he “Pay at Pump” system. The driver had inserted a card and had £100 holding sum debited. The pump was supposed to see him charged with the cost of the fuel and his £100 returned. It failed to charge for the fuel but his deposit was returned in full and he didn’t notice this until after QDR had become involved. Again, QDR were not interested. I would imagine PMF operate similarly.
My view is that these charges can only be levied on a contractual basis and to do that PMF would have to show who was party to the contract. I don’t see how they can do that in most cases. Only after they have done that would the terms of he contract become relevant.
"...he first told me I'd have to pay the fine.
He seems as legally ignorant as PMF seem to be. In general, only courts can impose fines.
I take it Morrisons now know that you were the driver at the time?