A couple of things come to mind about this discussion thread:
1) what kind of insurance policy does not cover an act of god - that is bout half your insurance coverage - I would be looking for another insurer as damage from storms and falling trees and such are a substantiall part of what many people are cuying insurance from.. Granted,, earth movements and groundwater are commonly not covered, and flooding is covered by FEMA Flood Insurance and war, riots and nuclear accidents are usually not covered, but pretty much everything else usually is or can be.
2) On the "negligence" issue - taking pictures is fine, but unless you have dated proof you notified him you considered it a threat and asked him to abate it, you will never prove negilgence - he can just say he did not think it was going to fall down, and that an unusually heavy wind gust (most likley to fail in a wind) was what caused it to fail, so is an act of god and not his responsibility.
3) this is like one case I consulted on a legal case for in a hillside subdivision, where one owner (the plaintiff) saw cracking on the steep fill hillside above his house on his neighbor's land, and pointed it out to the neighbor whose land it was on and mentioned it to neighbors and friends for a couple years, till it finally failed in a heavy rainstorm and took out his entire house and all vehicles. He tried to sue the neighbor on the basis the hillside was maintained as a hazard - lost case in about 5 minutes because while he had pointed out the cracks to the neighbor, his (the neighbor defendants) attorney pointed out that the plaintiff had never identified it as an imminent threat or asked that it be abated, and since the landowner defendant was not a geologist or civil engineer or earthwork contractor he personally had no reason to know or believe the cracks were anything more than the fill drying out and shrinkage cracking. To prove negligence or responsibility, you generally have to be able to prove the defending party ignored a known or specifically identified risk or danger, or willfully took an endangering action. In the case of this tree for instance, unless specifically pointed out as a threat and asked to abate it, the tree owner would likely only be liable if he were a logger or arborist with knowledge that it should be considered dangerous.