Well, it is their data.
The word "their" is overloaded, it could mean "thing I have the legal right to", or, "thing I have in my possession right now".
The latter condition is clearly true. It's their data.
If you pretend the other definitions of possession don't exist and claim "aktually it's not theirs they don't have rights to it" then that's on you for faking an incomplete understanding of language.
It's their servers sure, but if you download something under a license that doesn't grant you ownership, then it isn't yours.
You are being granted a license to use the data.
Well, but if it’s the latter definition, then the AI didn’t train on their data, since the companies took possession of that data before doing a training run.
It’s only the former definition that would allow an AI model to have been trained on someone else’s data