I trust my insurance company, so I would go with whom they suggested. However some companies want things done so it is the least expensive for them. You can always check with the Better Business Bureau or Angie's List and see if the company they are suggesting is any good.
It is good to go with a contractor that your insurance adjuster suggests to deal with your roof with hail damage. Finding your own contractor may be tricky because your insurer may deny any other claims if the roof is affected by other damages.
..Always submit about 5 estimates from different companies that You have researched.Aim for Quality and a Fair price.Compare their Quotes.Make copies of these estimates,keep some for yourself-then Submit to this insurance guy.Westie.