I think your understanding of generative AI is incorrect. It’s not just “logic and RNG”...

If it runs on a computer, it's literally "just logic and RNG". It's all transistors, memory, and an RNG.

The data used to train an AI model is copyrighted. It's impossible for something to exist without copyright (in the past 100 years). Even public domain works had copyright at some point.

if any of the training data is copyrighted, then attribution must be given, or at the very least permission to use this data must be given by the current copyright holder.

This is not correct. Every artist ever has been trained with copyrighted works, yet they don't have to recite every single picture they've seen or book they've ever read whenever they produce something.