The AI companies training their models are going to refer to it as their own data, once it's on their servers.

Taking someone else's car illicitly is theft, because theft means taking with intent to deprive the rightful owner of it. Copying can never be theft, only moving can be theft, because only moving it could deprive the rightful owner of it. An illicit copy is merely copyright infringement or a breach of contract or various other concepts that are not theft despite people sometimes using that word as shorthand. It's YOUR illicit copy, not the rightful owner's illicit copy.

> If you steal my car, no who knows it's stolen would say it's "yours".

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.

> The data was taken without license/rights/approval. It's stolen.

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.