Glossing through the paper, it seems they're noting this issue but kinda skipping over it:

In fact, it is clear that approximation capabilities and generalization are not equivalent notions. However, it is not yet determined that the reasoning capabilities of LLMs are tied to their generalization. While these notions are still hard to pinpoint, we will focus in this experimental section on the relationship between intrinsic dimension, thus expressive power, and reasoning capabilities.