Yes, exactly, if you ignore all definitions of "yours" that involve possession then it isn't "yours".
But no one else is obligated to ignore the definitions of words that you're choosing to ignore, so the rest of us will go on saying it's their data.
Guess what, the AI companies training their models aren't going to include themselves in the "rest of us"
If you steal my car, no who knows it's stolen would say it's "yours".
We're not talking abstract language concepts, this is a specific case. The data was taken without license/rights/approval. It's stolen. AA calling it "our data" is disingenuous. Legally it isn't theirs. While you could use "ours"/"theirs" loosely in English, they knew it wasn't true in a legal sense when publishing this.