Ugh... what a bunch of monkeys you've got swinging wrenches. Take your car out of that shop and bring it to someone that knows wtf they're doing. It sounds like they never bothered to look at your spare tire and assumed it was a "donut" tire, aka a space-saver spare tire. E34s came with full size spares on matching rims, so if you ever had a flat you didn't have to look out of place.

They didn't know what an H rated tire was? At a tire shop? I would have driven out of there on the damn flat.