I had a similar experience with UPS recently, though as a shipper, and it wasn't terribly encouraging. Here's the somewhat-abridged version:
The seller received the amp--a Bogner Twin Jet--in damaged condition. Specifically, the head box was split completely through at one corner--clearly the result of having been dropped from a height of several feet and/or repeatedly run over by a steamroller. Since I had sold the amp through Reverb and wanted to protect my seller rating, I immediately refunded him the full purchase price and filed a claim with UPS. Someone from UPS picked up the amp (and all of the packing material) the next day and returned it to their facility to verify that 1. it had, in fact, been damaged and 2. it had been packed in a manner that conformed to the company's (preposterously strict) packaging standards.
Fortunately, I'd followed my usual practice of having the amp "professionally" packed by the folks at my local UPS Store. Why? In my experience, this the only way to virtually guarantee that UPS will honor any damage claim for the full insured amount. Otherwise, they will almost invariably refuse to honor the insurance, citing "insufficient packing." It doesn't matter if you pack it in a Swiss bank vault inside of a Bradley armed personnel carrier--to them, it's "insufficient."
I figured that would be the end of it, but no, instead of scrapping the amp and sending me a check for $1600 (the amount for which I'd insured it), they sent the amp back to the UPS Store and instructed the manager there take it to a local electronics store for a repair estimate. But in another fortunate turn of events, the store manager by now was as fed up with UPS corporate as I was, so he found a shop that would declare the amp just short of un-fixable, just to move the process along. That approach actually worked, and roughly six weeks after filing my original claim, I received a $1300 "repair cost" check, along with the amp, which, aside from no longer having a head box, worked just fine.
(Note that I'm leaving out the part where they made me send them something to prove that the amp--which I'd already paid to insure for $1600--was, in fact, worth $1600. But yeah, that happened too.)
So the lesson here is, never, ever, ever ship an amp, and if you do, be sure to pay the extra $25 or so to have the shipper pack it. At least that way, you're pretty likely to get your money back in the not-at-all-unlikely event they "mishandle" it, even if you have to wait six weeks and jump through numerous hoops to do it.
Also, it turns out Bogner builds a pretty sturdy amp. I subsequently bought an NOS head box from someone here on RT, stuffed the TJ chassis inside, installed new tubes and resold the amp locally (disclosing the prior damage, naturally).
Circling back to your original question, I'm of the mind that it's always the shipper's responsibility to provide a refund if the item arrives damaged. Hopefully the guy from whom you purchased the AX8 agrees.
I filed a claim with UPS but there was a lack of communication for awhile since UPS and the UPS Store are separate entities.