Skipvia is on the right track - rice is an illusion. What one perceives as rice may not be "the rice", but an illusionary construct of the rice-seeking mind. If we did not seek rice, would rice exist? I believe only pasta has an actual existence.
Well, if you want to go all Kantian on it, you could say that white is merely our outward perception of the phenomenon of rice, a construct that we can't apprehend phenomenologically so we are limited to describing our experiences. White isn't rice, but it's inseparable from it.
But I think it's a beautiful and fun metaphor that means "really really close." I wish I had made it up.
I'm not sure it needs an etymology, skipvia! It's pretty clear what it means, and it probably came from someone trying to avoid saying another common phrase with a very similar meaning, but much less politeness: "like flies on shit." Given the God-fearing character of many southerners, I can see why "white on rice" became more popular!
Plus, it's just less gross and more creative. I like this phrase a lot.