Most package delivery companies as well as the post office wish to deal with the shipper with respect to damage in transit claims. And often, the shipper has no inclination to get too involved as they already have their money and the item is no longer in their hands. This is true even in those instances where the problem is attributable to the sellers deficient packing.
On the other hand, the recipient is very interested in the claims process since they are the one hurt by damage in transit. Typically they would very much like to deal directly with the package delivery company and get things resolved as quickly as possible.
For me, the solution has been to have the shipper act as an agent for me, and for the record reflect me as both the shipper and the recipient whenever items of value to me are shipped to me. Taking this approach puts me in the driver's seat when dealing with package delivery companies and damage in transit claims.
Like mileage, your experience may vary.