Countries do search. Whether or not they ought to be searching is a completely different question. Whether or not there are the appropriate oversight mechanisms, safeguards, and protections when they do conduct those searches is also a different question.
Can the NSA engage in widespread surveillance, and can some of our own agencies assist in that? Technically speaking, we know the answer to that. They can, and we know that they do.
I don't think that answers the legal question, and I don't think it answers the moral question either as to whether or not they ought to be doing that. Even if you conclude that they ought to be doing it in appropriate circumstances, whether or not we have the appropriate safeguards and oversight as part of those searches....