Yes i'm confused but maybe not the way you'd think :)
I guess "non-governmental" says it all. WTS's intention has never been to partisipate in making politics in the UN. The purposes for WTS to use the UN's library or other facilities has been to promote the spreading of the Bible thuth by being aware whats going on in the world. WTS has since it's founding cooperated with several institutions, even political, to collect and change information, to keep the Bible truth heard. Working in the name of religious rights can no way been seen as making politics.
God himself is about to use the UN to destroy false religion, so why wouldn't WTS use it somehow to make God's word known? UN is a worldwide institution and Jehovah may use nations behind it for his own purposes if He chooses so (thou Satan's rulership over the whole world), (Romans 13:1b). WTS has to operate with these institutions and try to follow international laws as close as possible. But ist's duty tell about God's plans about the earth, not to drive polical issues.(John 18:36)
As WTS announced, they cancelled that so called "NGO" deal after the UN had made big changes into it, making it look like an oblication to stand behind all goals of the UN, including political.