I know that there is a wide disparity in estimates for this kind of work. Just today, I had a large maple in our back yard trimmed to remove large (12-18" diameter) branches over the house and garage, a lot of dead and dying stuff and add cables to shore up a couple of other places. Estimates ran from $2,000 for just removing the 2 branches that I wanted gone to $700 for the complete work package described above. The estimate included my choice of the wood sawed into 18" lengths and stacked for my fireplace, or completely removed from my premises.
I don't know how to answer your insurance question, but my advise is get plenty of estimates and talk to the people while they are estimating. Talk to enough of them and you can get a feel for who is BSing and who is not.