So... you're saying the southern raider base isn't home of the Khans? It wasn't even in FO2, so no way it's run by Bishop's mercs.
It seems the devs thought the mercenaries payed by Bishop are the Khans from Fallout 1, and because of that they added the Southern Raider Base, which was the original Khan outpost. But they are not the Khans, they are just some mercenaries... Now, if the devs, after some update, decided to change this NPC faction so that they aren't called Khans anymore (changed dialogues, etc.), it wouldn't be "wrong" to still give them that Southern Base: remember that after the Vault Dweller raped the Khans, they
left their original base. This means they abandoned that place, and it could have been taken by the mercenaries after some years.
What's more, I don't understand why this NPC faction is called "Raiders" when they actually aren't Raiders, but some mercenaries which at that time were being payed to act as raiders.