Edit: I just reread the OP and finally I understand the situation. D'oh! (slaps forehead)
If the neighbor's tree fell on your parent's yard, and they are offering to pay for half of it, your parents should take that deal.
~ ~ ~ ~ ~ ~ ~
Ummm- get an expert in here, but I'm not at all sure the situation is clear cut. This whole area derives from English common law, which basically says that any branches of [strike]your[/strike] a tree that overhang a neighbor's property can legally (though perhaps not wisely) be cut off by that neighbor. Similarly, any fruit falling from your tree into their yard is theirs. Any branches falling off into their yard are their responsibility. If [strike]your[/strike] their tree falls over and lands in [strike]their[/strike] your yard, I believe it is on [strike]them [/strike] you to get it removed and cleaned up. Up to the property line, at least. If they really wanted to be pis*y, I suppose they could leave [strike]the bottom trunk and root ball[/strike] half of the tree for your parents to remove, and take care of only their half. Was it a property line tree? Those are especially problematic. You know how much a good surveyor charges these days? In the low thousands, if I recall correctly.
But here is where it gets a little dicey- if they (your parents) knew ahead of time that the tree was in ill health, a leaner, rotten, etc. and they had [strike]warned you, [/strike] warned the neighbors, and then it fell on their yard, in that case they could [strike]come after you[/strike] go after them for any damages. This stuff can get real complicated. What if they didn't say anything, but they lie in court and claim that they did? Ah, but nobody ever lies in court, right? :coolmad:
I'm not at all sure that [strike]the neighbors[/strike] your parents have any recourse. They may have to just suck it up and have the tree removed themselves. They may or may not win in court or through their insurance to recover expenses. A trial is not about 'truth' or justice or fairness, it's simply a contest to see who has the better lawyer. The "share expenses" route may ultimately prove extremely wise, and the least expensive way to go. It is real hard living next to folks who hate you. Food for thought...
True, it was an 'act of God' and probably totally not under the control of [strike]your parents-[/strike] anyone- but sometimes peace is beyond price, and greatly better than the alternative. Depends, I guess, on whether Hitler and Chamberlain are involved. ;-)
~ ~ ~ ~ ~ ~ ~
Personally, I'd try to not report things if they can be remedied fairly cheaply. On the ground? Cut it up, chip branches, stack rounds, split cost, done. Insurance companies love to cancel policies and jack up rates on a whim. I save the insurance for the big stuff, not the trivial stuff. I know a friend who got canceled by their home owner's insurance company for too many little claims.
If either family has already reported this to their insurance agent, then the two companies will work it out. It will be a hit on your parent's insurance claims history, not the neighbor's.