I think it's tantamount to bribery.
The fact of the matter is, Ford quoted for a piece of work and that price was agreed, the work was carried out, and the payment made. Contract over.
Now it is found that the amount was incorrect. To provide the correct documentation (which arguably should be the glow plug at price £0 - Ford business practice would require this), Ford want Olly's mum to pay for their mistake so they can raise an invoice for the full value.
Interestingly, they don't seem interested in pursuing her for the price of the glow plug otherwise....