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.
(I really hope that was an intentional reference or this won't make any sense.)
That's incorrect. A license violation isn't theft. Theft deprives others of their property, that's not what's going on here. Intellectual property is a fictional "ownership" that provides value to society, but it is much newer and different than the actual ownership of property.
No one actually owns a collection of words or ideas or thoughts.
So with that in mind, circling back to whether possession occurs in such a way to make possessive language appropriate (being able to say "my data" after stealing data but not depriving the author of the data), my opinion is that the copy of the data that the author still controls is the author's data, and the copy of the data that the stealer controls is the stealer's data. It's the author's idea, but both parties separately possess the data (the data is a record of the idea).
The chop shop well might.
Or, if I steal your car, and then go on to use it daily for the next 10 years, at some point everyone I know will refer to it as "my" car even if they're all entirely aware it was stolen.
> they knew it wasn't true in a legal sense when publishing this
I'm not sure why you're expecting the operators of a pirate site to use legally rigorous terms to refer to themselves in a blog post. This is an error in your expectations, not their terminology.
I found an abandoned bicycle 10 years ago. I have since replaced nearly all parts of it. I would give it back if you can prove it is yours but who owns the bicycle of theseus is more of an opinion.
I refer to it as my bicycle.