Only sort of, because some countries have very weird ideas of what a "judicial process" is.
>I'm certainly more comfortable with it than being subject to the whims of the US government and its 3 letter agencies.
That's fair, but I think it's a mistake. In the worst case the European system grants a village cop in another country the authority to conduct extremely intrusive surveillance on you.
Criminals can easily co-opt this system and steal your crypto or whatever, a far more realistic threat for most people than the NSA.
