Can you find out who a company's insurance is with?

Title says it all really. I want to make a claim on a company's insurance for damaging my carpets - they are being difficult. They admit the claim but won't pay and won't pass bill onto insurance company either.

forums.handbag.com/showthread.php?t=440457

Travel companies find insurance an adventure

Sixty-year-old Anne Mize has made more than 20 trips to such exotic locales as Belize, Botswana, Zimbabwe and Tanzania in the last 30 years.

story.100.com/?rid=8505095&cat=7efe203e304dfafb