SO, because the game was more light-hearted, this make it a Final Fantasy game? I'm sorry but this does not make the cut IMHO. Phantasy Star (the original) didnt have a deep plot too, and can you call it a Final Fantasy clone.
And even while being less dark than PSII (which is not totally a BAD point in itself), it's still darker than most Final Fantasy. Well maybe PSIV is not as "dramatic" as FFIV...but you know what? This is why it really can't be influenced at all. I'm sorry. But having played FFIV myself at least 3 times in my life, I still can't figure out the similarity between the two games outside that they're both 16 bits 2D turn based RPG.
But at least you have given reason as to why you think so, and for that, I'm happy

It still does not shake my opinion though that there's nothing FF in PSIV. Maybe someone else have others opinions?