It seems the skill cutoff is based on the lvl 96 C+ skill cap of 357, but all that means is that PUP wouldn't be able to unlock it until lv. 98.

There's only a 10 skill different between C- and C+, which is easily covered by skill merit upgrades or even a single piece of gear, so I agree that any C- skill and above should be able to unlock it. (As long as they have the 357 skill natively.)

DNC only having 1 WS is not surprising, as they only have one combat skill above D, unless SE decides to drop a bomb on us with Throwing weaponskills.

Extra jobs on WS based on skill 357+ and level 96+ :
Exenterator (Dagger) : DRK (97), PLD (98), PUP (98)
Requiescat (Sword) : BRD (98), DRG (98), NIN (97)
Tachi: Shoha (Great Katana) : NIN (98)
Realmrazer (Club) : DRK (98)
Apex Arrow (Archery) : THF (98)
Last Stand (Marksmanship) : NIN (97)