I’m sorry to hear of your experience. I would agree double box or triple box audio equipment…with adequate packing inside. The UPS stores I am aware of only sell plastic peanuts or bubble wrap for packing. As these are 99% air they have limited use. They are for light items and heavy items will typically not survive if they are the only packing. UPS guidelines require that packages be able to withstand a 3ft drop on any side, corner or edge.
If you paid a UPS store to pack and also insured an item, I would think the store is responsible to meet the UPS packing requirements. So if UPS doesn’t pay for the damage, then they should. Since they’re local for you, small claims court should be an option.
For any claim there has to be visible damage to the box. I would also guess that any damage to the contents that is not visible - like a rattle - wouldn’t be covered by insurance. I would add that to me it is very logical that UPS would require the shipper to adequately pack an item to receive an insurance claim. So I wouldn’t consider that to be ‘buried in very fine print’. To me as a shipper it is extremely crucial that I pack an item adequately to make the journey safely under normal circumstances. I try to go the extra mile. But then I don’t usually buy insurance.