I don't think that FFXIV was being developed originally to be part of FFXIII as they would need to use FFXIII's world if that were the case.
Versus and Agito XIII don't use XIII's world, either. Supposedly, the only tangible link between the games in Fabula Nova Crystallis is the involvement of the titular Crystals; FFXIV could easily have started out as part of the project with only that stipulation.