I really think you give FFIII too much credit for what it did. You might as well claim the original FF was the start of the job system. The only difference was you could switch which characters were physical and which were magical. Everything in FFIII ended in either Ninja or Sage. Physical attackers all became Ninjas, and magic users Sages in the end because they were simply better than everything else. Having any meaningful gains after switching a class was not present at all.
Really as we talk this out I think the right statement is that FFT took FFV and Ogre series respective systems and refined and melded them together. Neither game has all the elements present to create the system, but the best parts of both seem to have ended up in their "child" for want of a better term. It is obvious that some of both series legacy would be present as the game was made by veteran's of both of those series.
I'll concede the point, then.