It's possible that statutes differ, but in 35 years of insurance experience here is how I've seen it.  When negligence is not involved and the tree falls due to an "act of God" such as wind or disease (let's say previously undetected or unacknowledged), the owner of the property where the tree lands is footing the bill.  My tree blows over in a hurricane onto my neighbors fence and lawn - they're paying for it.  If I negligently cut it with a chain saw then that's a different story.  As to whether insurance is paying for the loss in the wind scenario, one needs to consider whether there was damaged property or not.  In many cases landing on the lawn will cap out how much might be paid ($1,000 is common), if any, under a homeowners policy.  Also, was the damage in excess of the deductible applicable to wind?  The unlucky homeowner sustaining the damage would typically see their policy pay for the damage to their fence (less depreciation in most cases) minus the deductible.