Yes and no.

They are arguing that the current copyright laws do not forbid training. And they are arguing that they need to train on copyrighted data in order to be able to make an effective tool (and make money).

That second part of the argument is there because, so far as I know, nobody has ruled (in any country) on the legality of using copyrighted material as training for LLMs that will then produce commercially-available output. So the first part is a claim, but it's not a ruled-upon claim. It's not a claim that OpenAI can count on a court agreeing with. So they add the second argument, which amounts to "please interpret copyright law that way, and if the courts don't, please change copyright law that way, or else we can't sell what we make (and therefore can't make any money)".

I take no position on the first claim. All I'm saying is that the appropriate response to the second claim is, "So what? The world doesn't owe you a living."