I just dealt with this last week and UPS does ship ammo from their hubs but they won't ship from UPS Stores or their commercial affiliates. Unfortunately many of the workers, even at the hubs, do not know their policies so I had to inform them of what they would be doing. I had called their national hazardous materials hotline before going in so I would have everything covered. The kids working there were clueless and intially balked so I had them call their supervisor, who had to call a regional office, to get clarification. Anyone can walk in and ship ammo that is .50cal or less if it is labeled appropriately, which you can do yourself with a Sharpie. In order to ship handguns you have to hold a certain type of account, that I didn't have. FedEx has the least restrictive gun shipping regulations but their ammo regulations are ridiculous... don't mess with it.
Bottom line: when shipping ammo go to UPS. when shipping guns go through FedEx unless you have a UPS account.