Client calls with this exact problem and says, "I am waiting for my neighbor to come home to find out who his insurance company is." Um, Mr. client, this claim will be on your homeowner policy, not your neighbors. in insurance terms, we call it "Act of God", as nobody was negligent in having that tree fall. Doesn't matter who's land it was on, neighbors, the towns, the city...wind or soil erosion caused the tree to fall. Can't blame it on the neighbor or the town, it happened!
So the claim is your, whether fail or not. No negligence was involved in your homeowner claim.