Here's how I look at the UN affiliation as hypocritical and damning to the WTS:
The average JW cannot, without penalty(DFing), join the YMCA or YWCA. If I, as a JW, decided to join the YMCA, not for so-called Christian fellowship, but for the sole purpose of using the gym facilities, because they are the best in my area, I would be disfellowshipped for having joined together with Babylon the Great. A true Christian(JW) cannot and would not do this. There is no room for discussion; quit, repent or be disfellowshipped.
The WTS joined the UN as an NGO. Not to fellowship with other NGOs or help do what it is NGOs do, but to use the library(their story). Whether it's to use the library or not, they have linked themselves with the Wild Beast. They have allowed themselves to become entangled with the world's politics. When pointed out to them(found out by press and others), they quietly quit and gave the library card excuse. No repentance was shown for their sin. They have condemned themselves not only by becoming an NGO, but by quietly, lyingly, excusing their actions as a sincere attempt to gain access to a library without any remorse or chagrin.
That's how I refute their excuse. If the avgerage JW can't use that excuse, then how can the WTS?