I would bet your deductible is around $300- $400. If you find that this repair is ligitmate and a good contractor, I would go ahead with them and forget the insurance company. I have always felt that using the insurance company will only cause down the road problems when you really need them and when your evaluation comes along.
YOur repairs sound relatively simple, its the already damage behind the walls that I am concerned about. Opening that up and drying out and killing the future mold and all is the real problem.
from what you have described, and if you have any handyman experience at all, you should be able to fix this problem yourself. Peel back that course of siding that butts up to the brick and install step flashing or one piece two inch drip edge flashing and you should be fine.