Their idea is that the EU cloud's corporate structure is completely independent, so AWS US isn't a parent company' so the CLOUD Act doesn't apply. They aren't a local subsidiary, they are an independent company licensing the AWS tech stack to operate fully independently on their own hardware - which just happens to also have a license to the AWS name.

It's a rather clever idea, and it essentially prevents EU government organisations from excluding them from tenders by requiring EU-based ownership. It obviously won't convince anyone with half a brain that they are genuinely independent, but the government lawyers are going to have a really hard time writing tenders in a way which excludes them from participating.