Yeah. Ogre Battle differentiates itself considerably in that classes work almost like skill trees in later games, and the stat growths you get in different classes more easily facilitates switching to (and being effective in) other classes. A Fighter might need 14 Strength and 12 Def to become a Knight, for example, whereas it might need 15 Strength and 10 Def to become a Berserker - and the Knight has better growth in defense than does the Berserker, which means it will be able to switch into the Paladin class faster.
I'm not saying OB doesn't take cues from FF3 or anything, I honestly have no idea on that front.
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.