You - no, you - no, you.....

Following the recent storms, a tree on property A has been blown over and landed on property B causing damage.  Who is responsible?  Common sense and my (admittedly old and possibly out-dated) legal knowledge says the owner of property A.  But they - or more to the point, their insurers - say that as all the damage is to property B, it is for them (or their insurers) to sort out.  Meanwhile the occupant of property B has to put up with the fact that they have a tree poking through their kitchen ceiling or wherever.  Make you sort of wonder why we bother with insurance, doesn't it?