From a carrier's perspective, if the roof was not damaged by a covered loss (such as hail or windstorm), then only the ensuing water damage to the structure should be covered by the policy.
Interesting perspective. My experience is that without a covered loss, the resulting damage is also not covered. On the flip side though, this has always been because of lack of routine maintainance, i.e., the roof is worn out or the roof tiles haven't been maintained and have cracked.
In this case, there was a very recent inspection which didn't show any issues to be taken care of. Due to this, I don't know how the claim would come out, especially since I don't know who the carrier is and I don't know anything about New York.
Dan