I also had a problem with my UPS center (not a 3rd party UPS). The first time I sent out a BP rifle, no problem, the second time I sent out a BP rifle, minor problem, the same counter guy who handled the first shipment told me that a UPS security guy had told him that he wasn't supposed to be accepting BP rifles unless I had an FFL. I very nicely told him that the UPS security guy didn't know what he was talking about. I further informed him that if he wanted to I would wait while he contacted the security guy or the local police, and that I would prove it to him. The counter guy was really polite and said that he would accept the shipment, but if there was a problem, that they would call me. I told him that would be okay with me, and I told him that I had a copy of the Law book that specifically covered that part (which stated that BP rifles and pistols are not considered firearms), and if the security guy wanted to get a copy, I would be glad to give him the section of the law, and that he could look it up. I since went back to the UPS facility and sent out another BP rifle with the same guy at the counter, I asked him about the "problem shipping BP rifles", he said that he mentioned it to the security guy, and to his credit, the security guy said that he was wrong.
In your case it would help to have a copy (print out the reg. that quick gave you a link for) of the UPS regulations to show them, unless they were a 3rd party UPS store, then they wouldn't touch it with a ten foot pole.
Your best bet is what quick recommended, using the USPS, less of a hassle, and I found out it was also a lot less expensive, which was a bonus.