While UPS may know how to pack the guitar case in a shipping box, I certainly would not leave it to them to properly pack the instrument in it's case. The most critical issue in packing a guitar or bass for shipping, air travel, or any situaion where someone else is handling it, is peghead support. Talk to any luthier that does repairs and they'll tell you that by far the most common damage from shipping is a broken peghead. The overwhelming majority of instrument cases support the neck only and the peghead hangs out in midair where it is susceptible to the whiplash caused by the crate falling, being thrown, shifting in the cargo hold., etc. When shipping or travelling by air, be sure to add bubble wrap, padding, foam, old T-shirts, whatever, inside the case to give support to the peghead.
Bill, tgo