They can assert what they want, they have no way to enforce it.

Pretty funny you're jumping straight to warfare. This proves why Americans cannot be trusted.

In any case, it's better for me that the Americans will need to start a war with the EU to get at my data instead of just giving it to them.

I'd argue that placing faith in any large institution is folly. Especially when that institution has a bunch of perverse incentives to act immorally.

Any nation with any amount of leverage has abused it.

We agree, I'm not saying anything is good or desirable. Just pointing out, this is how they achieve overreach: coercion.