Insurance does not typically cover the damage and line of sight. Insurance does not pay to match old to new. They might pay for gross mismatch, such as a particular roofing material not being made anymore or a siding product not being made anymore. It doesn't make financial sense for an insurance company to have to replace an entire roof for 5 damaged shingles. Or an entire fence for only 3 or 4 sections being damaged.
You definitely need to call the insurance company ASAP. The insurance companies have a right to inspect the damage and verify the claim. They might pay for the damage after you have fixed it, but it's not a guarantee. If they do pay for it, with it being a liability claim, they should pay you replacement cost. However, if your homeowners insurance comes into play, a lot of major companies pay actual cash value for wood fences, which accounts for depreciation. Plus, it might not even come close to your deductible. Next time, call the insurance company first before you do anything to the damage.