That is BS. Fed Law (the only one that is important in this case) allows Interstate shipment BY THE OWNER of any gun to any FFL, mfr, gunsmith for work/repair. USPO prohibits anyone (Fed Reg or law) other than Dealer from shipping any handgun. Thus, you need to deal with UPS or FedEx . . . both of whom have internal policy that requires air shipment for handguns since they can't control their parcels from being stolen by employees (but this is NOT law, only company policy).
You MUST ship by either going to a UPS/FedEx depot (no storefronts like Kinkos or UPS Store), have UPS/FedEx pickup at your house/business, or it APPEARS legal (and OK by their policies) to setup a pre-paid account online, create your own shipping label (properly declaring contents) and handing the package to the local UPS/FedEx driver. I have done "some" research on the last idea, but never got or asked for a "ruling" by either company that this was acceptable or not (it would be a company policy thing).
I have shipped handguns to the mfr for repair before with no hassles. I have also brought the defective gun back to the dealer I've bought it from and had them deal with shipping it back (at no expense to me).