No, it isn't. Nothing about training a model requires this. You're thinking of copyright, which does treat information this way.
Well, AI and Copyright are both related things that people created, so it's certainly relevant. I don't think the person you're responding to misspoke.
Sure, I'm conflating the tool w/ the people building the tool - but imo muddling the distinction is good, because the hard distinction is what tricks people into an unthinking mode.