The piracy comes first, and it's exactly the same thing. GenAI Corp. can't train models on illicitly obtained media before illicitly obtaining said media. And that very thing is already what private individuals got and get sued for millions over.
The GenAI Corp., having gotten away with that unpunished, then goes on to commit further violations by commercially exploiting the media with neither a license to do so, nor any intentions to pay the rights-holders for their use.
By the media conglomerates' own math, these GenAI companies should all be drowning in lawsuits over kazillions of bajillions of dollars.