I've never seen mention of requiring the pistol case to be inside another bag. I think it can be inside another bag, but a hard sided case holding five pistols and 11 pounds of ammunition is a large case on its own right and too big to fit inside another bag unless you just really like paying oversize bag fees.

FWIW, here is what DL says this morning:

Shooting equipment is accepted as checked baggage.

When checking a firearm, you must:

Declare to the Delta representative that you are checking a firearm (If a Security Checkpoint is prior to the Delta ticket counter, you must declare the existence of a firearm to security personnel.)
Present firearm(s) unloaded and sign a "Firearms Unloaded" declaration
Lock the firearm(s) in a hard-sided, crush-proof container and retain the key or combination
Maintain entry permits in your possession for the country or countries of destination or transit
Ensure small arms ammunition is packed in the manufacturer's original package or securely packed in fiber, wood or metal boxes
Firearms transported to the United Kingdom as checked baggage require a permit from the United Kingdom. The passenger must contact the United Kingdom for more information regarding this permit.

Ammunition in excess of 11 pounds per passenger or that contains incendiary projectiles is prohibited.

Rifles
Delta will accept firearms and shooting equipment packaged as follows:

One gun case containing up to a total of four rifles or shotguns, plus shooting materials, and tools
One gun case containing up to five handguns, one scope, and tools
One bow and quiver of arrows and maintenance kit enclosed in a case or container of sufficient strength to protect the bow and quiver from accidental damage

An excess baggage fee will apply to cases containing more than two rifles.

Shotguns
two shotguns
two shotgun cases
11 pounds (approximately 5 kg) of ammunition
An excess baggage fee will apply to cases containing more than two shotguns.

Pistols
One pistol case containing:
five pistols
pistol telescopes
noise suppressers
a small pistol tool case
11 pounds (approximately 5 kg) of ammunition
An excess baggage fee will apply to cases containing more than five pistols.

and don't forget this fun DL fact I just found, Mr. Cooper: "Sport parachutes are accepted as carry-on baggage"