I think it’s agreed that this is about liability.
If the OC is liable for the damage caused (including to any lot), the OC has to pay for the repairs. The OC’s insurance will hopefully cover the OC’s costs. But if it doesn’t, the OC is still liable.
So the question to ask the OC is “Why isn’t the OC liable for the damage?”. And if the OC’s answer is “It’s because the OC’s insurance policy will not pay for it”, that’s the wrong answer. If the OC’s answer is “It’s because the OC was not negligent”, that’s a different matter.
I’ve had a closer look at one of our claims that our insurance company paid. A building defect allowed water to damage both common and lot property (including lot paint). The insurance didn’t cover the defect repair but it did cover the damage it caused, at least to common property, as this was not a “lack of maintenance” issue. The water damaged a lot’s ceiling plaster – which is common property. It wasn’t possible to repair the lot ceiling plaster without then needing the whole lot ceiling to be repainted – the paint being lot property. It was therefore probably an example of a common property repair (the lot ceiling) necessitating the repair of the lot property (the paint).