This is what he says:

"It is a different view of the world, a different way of looking at the world. That's why I prefaced my answer to your question with the story about the roundness of the world being one way of viewing the world. An evolutionary geological perspective is one way of viewing the world. A different way is with the six days of creation. Truth is in our minds. If we are sufficiently broad-minded, then we can simultaneously entertain different ideas of truth, different models, different views of the world."

I don't think he's talking about separating beliefs into true ones and false ones.

The point of his discussion of the roundness of the world is that in order to say that, we are idealizing and approximating. Idealizing and approximating are things that happen in the mind, not in the world; that is why he says that "truth is in the mind," and in that respect he is right, even if truth is in things in another way.

Obviously the world was not formed in six days even in the way it is round. You cannot simply idealize and approximate in the same way and get that result. Aumann is aware of this, since otherwise he wouldn't say that you need a different way of looking at the world; you could look at it in the same way, as young earth creationists do. That makes it clear that he does not accept a literal six days; if he did, he wouldn't say you need a different way to look at things.

He was making a comparison. Idealizing and approximating are a scientific way to make statements about the world. Metaphor is another way, and that's what he was talking about. But metaphor is not simply about making false statements, so separating literal and metaphorical statements is not simply dividing between true and false.