Does the license plate number on the report belong to a truck matching the description? i.e., is it likely there actually is a mistake or are they just being.... recalcitrant?

What does your insurance company say? Normally they'd be the ones on the hook for paying for the repairs and then trying to get payment from the other guy's insurance. Although that may depend on your deductible and coverage selections.

Beyond that I don't know. Claims court?