Wow, does my heart go out to you, friend. I had a close cakll with a tree and a dually pickup, but fortunately only scratched up the side of the bed. So sorry for your bad luck, that sucks. Trees are funny sometimes, every once in awhile they do something that seems to defy gravity, or a gust of wind comes up on a still day...I'd echo the thoughts of previous posters and try to look at the side of "Thank God no-one was hurt..." Tree that big could easily have killed someone...
I'd also echo the thought that you should act like you presume that they'll cover it until they say otherwise. Insurance companies are the lowest of nthe low when it comes to trying to escape their obligations....Hope you make out ok
Mike