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You can read a book without your brain getting owned by the author.
It's perfectly reasonable to say it should be considered copyright infringement, but such cases are in the court now.
Disclaimer: I am not a lawyer.
"Training" doesn't really have a well-defined meaning, I could use your website to train something as simple as a histogram of word counts for an AI for example. Nothing about that constitutes copyright infringement under even the loosest definition of their legal concept.
Additionally weights from training and the AI's output are two completely different matters from a legal perspective as well.
If it's an accurate transcription and you don't have permission, then it's not legal. It doesn't matter if it's for money or not (or if it's from memory or not).
> Does it matter how faithful your transcription is?
Yes, it matters. Copyright covers the specific expression of an idea, not the idea itself.