None of them are true, Offerings and Gem Boxes can't be earn trough morphing. KatanaSoul can't be morphed but he does drop an offering after the battle and Boxed Set can be morph into Safety Bit or Tonic.

For your info, these are the 26 different patterns of item an enemy can have. The 3 first are the most common to find.

Antidote, Green Cherry, Eyedrop, Soft
Tent, Fenix Down, Warp Stone, Revivify
Dried Meat x4
Remedy x4
Mithril Blade, Mithril Helm, Mithril Mail, Heavy Shld
Gold Lance, Gold Shld, Gold Helmet, Gold Armor
Crystal Sword, Crystal Shld, Crystal Helm, Crystal Mail
Imp's Armor, Titanium, TortoiseShld, Imp Halberd
Ogre Nix, Tonic x3
Marvel Shoes, Tonic x3
Tintinabar, Tonic x3
Megalixir, Tonic x3
X-Potion, Tonic x3
X-Ether, Tonic x3
Elixir, Tonic x3
Gauntlet, Tonic x3
Genji Glove, Tonic x3
Safety Bit, Tonic x3
Exp. Egg, Tonic x3
Ribbon, Tonic x3
Flame Shld, Tonic x3
Ice Shld, Tonic x3
Thunder Shld, Tonic x3
Cursed Ring x2, Thornlet, Relic Ring
Cure Ring x2, Safety Bit, Pod Bracelet
Trump x2, Assassin, Striker

BTW, those info are not poping out of nowhere, they come from FF3usME utility (http://www.angelfire.com/pq/jumparound/index.html).