I wouldn't be messing about arguing with a customer and looking at a website at the side of the motorway. If already paid I'm doing it or not and then GTFOASAP.
Agreed, complete idiot of a customer and the terms seem fine considering your paying for the convenience of call out with equipment and danger of working in live traffic.
Altho TBF tyre is cheap Chinese thing replacing a Bridgestone, but he's right they are a stupid size and like a rubber band so probably an arse to fit.
Does it matter to get you home and off the motorway... the longer your on the shoulder more chance a HGV wipes you out...