A bit odd to see them all labeled "runs out of Europe". I understand why they do this, but it's not like European hosting is a bullet proof solution for invasive snooping or data requisition.
It's impossible to prove. I think the best you can do is a) no legal basis for that kind of thing, and even more importantly b) a citizenry that remembers totalitarianism and knows the importance of privacy rights.
Europeans in Europe can take countries etc to their local courts, or to the European Court of Human Rights, or the Court of Justice of the European Union. Europeans are not able to take any court case against the US government in US courts.