They don't. Unfortunately, you ran into something we see on the internet everyday; someone with only a little info.
The particular clerk you ran into doesn't know the regulations. He/she assumed everything they told you. It's a case of a small person exerting an authority they don't really have. This person looks for an opportunity to tell others "no" to give themselves the illusion they have power over others.
Next time you go, take a copy of the FedEx rules with you:
Prohibited & Restricted Articles | FXF Rules Tariff - FedEx
It says the box can't say it's a firearm on the outside. There's nothing about it being a FedEx box. Neither does it mention the speed at which it must be shipped. That is only covered under the federal laws.
**A side note** I find it interesting that FedEx won't accept stamps as payment for shipping something.