Two things are at play here. First, the seller typically files the insurance claim. Second, the buyer doesn't necessarily have to wait for the claim to be paid to get a refund - the buyer can open an "item not as described" claim with eBay and get their full refund from the seller. The seller than may get full or partial reimbursement from the post office.

A seller can file an on-line claim with the post office, but needs to have an internet account with them to do that. It's not complicated.

Link to post office on-line claims: http://about.usps.com/publications/pub370/pub370_tech_013.htm