I agree with your observation about the exact noise-free nature of the problem. It allows them to formulate the problem as "minimize complexity such that you memorize the X-y relationship exactly". This would need to be generalized to the noisy case: instead of demanding exact memorization, you'd need to prescribe an error budget. But then this error budget seems like an effective complexity metaparameter, doesn't it, and we're back to square zero of cross-validation.