They are signatory to a treaty that requires them to pay for damages. And they had no control over where this booster came down (except that it would come down between 41S/41N, roughly), so your "they would never allow" is incorrect.

China signed the Outer Space Treaty. Your rocket your damage your bill.

But how is anyone going to collect on the bill, if China doesn't want to pay?

Just quickly and quietly paying is likely cheaper than the international incident, the "China refuses to comply with treaty" headlines, and likely resulting souring of international relations.