The interpolation isn't really based on statistically occurring text. It's based on statistically occurring concepts. A single token can have many meanings depending on context and many tokens can represent a concept depending on context. A (good) LLM is capturing that.
Neither just text or just concepts, but text-concepts — LLMs can only manipulate concepts as they can be conveyed via text. But I think wordlessly, in pure concepts and sense-images, and serialize my thoughts to text. That I have thoughts that I am incapable of verbalizing is what makes me different from an LLM - and, I would argue, actually capable of conceptual synthesis. I have been told some people think “in words” though.