I think you're using the word "copy" incorrectly. What does it mean to "copy" a Youtube video? You are literally making a copy of it on your computer as you watch it, that's what watching a video is. You're also making a "copy" of it in your brain.
I'm not sure about literally downloading YouTube videos, you might be right about that.
At least under US law, the person downloading the images has to be the same one who trains the model, because giving them to another person is copyright-violating distribution.
To be clear, I'm just sick of corporations being free and clear to do things that would get the rest of us stomped.