No - I end up shipping handguns via ground all the time.
I am a FFL and previously worked at UPS for several years as a next day air supervisor. There is no law on how you have to ship a firearm except in regards to using the postal service. Many carriers have their own restrictions but it is not law.
UPS for non FFL's and FFL's
Firearms must be shipped next day air to a FFL. FFL # must be listed on package, and adult signature is required. You must take the package to a UPS center (ups store does not count, nor do drop boxes). Package must be declared as a firearm. FFL's may ship firearms directly back to the registered owner of the firearm (ex firearm was sent to FFL for gunsmithing or repair, it may be returned direct to customer.) If the customer has not dros'ed (dealer record of sale) the firearm then it must be shipped to the customers local FFL where it then can be dros'ed.
Fedex is pretty much the same but must be shipped priority overnight
USPS for non FFL
Non FFL's may only ship long guns (rifle/shotgun) and only within their own state. While it is not stated clearly the long gun must be shipped to a FFL unless the long gun is already dros'ed to the recipiant. The one exception is if the owner of the firearm is shipping a long gun to himself in the same state for the purposes of hunting. Then the long gun can be sent to a representative for this purpose. (ex you are going hunting by your dad's house who lives in the same state, you may ship him your rifle and then pick it up from him when you arrive. If sending a long gun out of state then it must be sent to a FFL. Long guns must be taken to a post office and no marking on packaging listing contents as a firearm. It's odd as USPS does not require non FFL's to state there is a firearm in the package.
USPS for FFL's
FFL's may ship firearms including handguns. A form 1508 must be filled out and brought to a post office with the package. The 1508 is round stamped and signed by the postal counter person and it is given to their supervisor. The package must not be labeled as a firearm.
We as a FFL mostly ship firearms usps priority mail insured. It is way less expensive than UPS. If the customer requests and pays we can ship ups next day air insured.
As far as our customers shipping to us we don't care how they ship as long as we get the package. Some FFL's will reject packages if they are shipped improperly (though the carrier).
If you ship a package inproperly though USPS I can see it being a legal issue for the sender. If you send it improperly through UPS or other common carrier and it gets lost then they accept no liability. Thus in the OP's question if his firearm sent ups ground get lost then he is SOL. Even if the package is insured $10k UPS is not obligated to pay at that point. The OP's FFL should of sent the package usps or ups NDA.