Well in my example the AI doesn't have to interact with the world at all. To pass the Turing test simply requires imitating a human, predicting what words they would say. You only need to know the relationships between words.

"Is it day or night?"

If literally the only thing you know is the relationship between words, but you have a perfect knowledge of the relationship between words, you'll quickly determine that "Day" and "Night" are both acceptable answers, and have no means of determining which is the right one. At the very minimum, you need a clock, and an understanding of the temporal nature of your training set, to get the right one.

A beautiful rainbow glimmering gently in the sky after a summer shower.

What do you see? What do you smell? What do you hear? What does the landscape look like? What memory does this bring up?

These are messages that the language is communicating. If an AI can't understand at least some of the content of the message then can it compose one effectively? I'm not certain it can understand the meaning from words alone, but we can certainly try.

Only knowing the relationships between words alone would just be a poor proxy for knowing the meanings of the words, e.g. what real world concepts the words attempt to represent. You might be able to get pretty far with this technique, but I would bet a lot of money you would not be able to get reliable, in-depth human level communication. The system needs to have an understanding of the world.

And then there is the fundamentally dynamic aspect of language, which strengthens the need for a rich understanding of the world that words describe and convey.

There are other tests for AI besides the Turing Test, some of which require more understanding on the part of the program. Check out Winograd Schemas: http://www.cs.nyu.edu/faculty/davise/papers/WinogradSchemas/... which hinge on understanding the subtleties of how words refer to the world.