No you don’t pay. Dealerships especially service departments often get wires crossed ( they tried changing for our last Mot)
A similar thread came up last week and I knew the information would come in handy (didn’t expect it would so soon) so I looked into it a bit for my own curiosity,
The key bit is the post from Jordan, and the guarantee to a courtesy car if 3 weeks notice (not all dealerships need this) having looked at links etc it is clear that a courtesy car is to be made available in various situations but at no point is payment mentioned. Some information reads different and slightly contradicts one another but overview is No charge
I would ring the dealership and say you’ve checked with Motability and they said thier are no charges, if they don’t budge then call motability and let them deal with it.
Its probably just that dealerships booking in process and the person making the booking wasn’t aware of any difference and just following procedures.