To clear up all of the myths here:
UPS guidelines specify that every shipment should have a minimum of 2" of packaging (bubble wrap, foam, air bags, but no peanuts or paper.. those are just fillers), with 3" for semi-fragile items, and as much as possible for very fragile items... it's their judgement after that.
If you send a package through an Authorized Shipping Outlet (Mailboxes, Staples, local place), you will have an easier time getting your claim paid, as they will do the grunt work for you. To get a claim paid you must:
Make UPS aware that the item was damaged.
In some cases, send the item to a UPS center for inspection (along with the original packaging).
Fax an invoice/repair bill for the item to UPS showing the value of the item to be at or above the amount of insurance.
Wait.
Takes 3-5 business days for them to cut you a check if your claim is approved, and then you just have to wait on the mail.
Josh