There are an entire list of reasons why a USA-centric internet is a bad thing even without the privacy considerations. Not least of which is the fact that the US is effectively worst-in-class when it comes to Internet adoption. And not coincidentally, also the most ravenously capitalistic society. To far too many Americans, the Internet is a profit mechanism, not an infrastructure.
Just to be clear (as someone working at one organization that helped develop these principles and the consensus around them), the principles were not developed or published by the U.N. They were created by a consensus of voluntary nongovernmental organizations from all around the world that work in the area of human rights.
Here, the principles were being presented to the United Nations -- not by the United Nations!
The answer is to not have to trust them. Unwarranted surveillance has to have two components. Proving that it has been stopped is effectively impossible, but what the legislative component can do is to delegitimize it. Passing legislation makes the statement that unwarranted surveillance is unacceptable, and paves the road for people to implement measures to thwart it without allowing the government to use the law to threaten them.
Then we have to set out to thwart it. Build into the network the technology to make surveillance as difficult as possible. Decentralization, end-to-end encryption, perfect forward secrecy, etc. etc. Because that's how you can trust them again: When the math proves they can't do it anymore.