One thing I don't entirely understand is whether having an EU-based server provided by an US company (Rackspace, AWS, Digital Ocean, you name it) makes any difference at all.
The companies are incorporated in the US, so subject to US law. But the physical servers are located in other jurisdictions, and sometimes US law conflicts with that law.
In practice, so far I suspect that the US law has won out, because other jurisdictions haven't known to fight it. In the future that might change, but... secret orders supported by secret laws enforced by secret courts can be pretty hard for other jurisdictions to fight.