It's not quite as easy as they pretend..
The key factor here is leverage. If Twitter US is the HQ and the EU leg is deemed a subsidiary, there is not enough legal separation, and a US judge can do, well, let's call it a Microsoft. If it's a wholly separate company, the picture gets ugly from a different angle: Twitter US should not have access to the data of Twitter, umm, "elsewhere" or "EU".
It will naturally be a total coincidence that both companies will pay massive licensing fees to some offshore entity, but I digress. As long as it's not quite clear what structure they put in place, I would doubt their own statements about not being beholden to US law.
Now, stepping back a bit - Twitter? Wasn't all that data public anyway?