Board Thread:Dark Souls III/@comment-17496033-20160419043701/@comment-4511886-20160419054828

Pretty sure Vendrick didn't forfeit the throne, but rather never reached it.

He was "not a king at all" according to the Shield of Want's description, which is also stated by Aldia. According to the lore of DaSII, only a "true monarch" could claim the throne, and thus choose whether to link the fire or leave it.