AM_dial: Glad you found out you got bad advice. You hopefully also learned a valuable lesson: agents don't always know about claims. It's always amazed me that the same agent that would laugh his rear off if I tried to sell insurance, thinks nothing of trying to advise people regarding claims...
BrianW- glad you had a good experience- that is the way claims are supposed to work. Just keep in mind that if you change one thing in that experience, it could have been very frustrating for you.
Possible change #1: Grumpy, inept, or just plain burnt out adjuster. There are 2 of these for every competent, courteous and professional one at some companies.
Possible change #2: Instead of a little water leak, you come home from work to find a smoking hole in the ground where your house once was. Now demonstrate the quality of your collection.
Possible change #3: Insurance company is struggling financially. Stock prices are down. They're trying to pretty up the balance sheets for a possible purchase by another company. New claims manager comes in and starts hammering staff adjusters to reduce loss ratios. Suddenly people aren't so willing to see your side of things.
Just food for thought.
Someone mentioned taking lots of pictures, and that is excellent advice. Take a ton of digital pics of your gear, your room, your software (take LPs out of the sleeves to show condition)-- put that CD-ROM in a safe deposit box, at your mom's house, or in your desk drawer at the office. At least then you'll only have to worry about replaceability, not proving you had the stuff, or its condition.
Sorry for being long winded.