How can a newspaper be good enough to cite in a Watchtower publication, but the same newspaper be condemned as declared forbidden reading?
I think it depends on how your worldview is shaped. If the idea is that the whole world is effectively against you (because it is under the control of God's main enemy), then you can claim that any good news has to be legitimate, since Satan is loathe to allow anything positive to be said. Conversely, bad/negative news or information cannot be true, since Satan would want to put the JWs in the worst possible light, and doesn't hesitate to lie.
If you point out the absurdity of this concept, you are likely to be bombarded with a flood of "what about this" objections and cherry-picked examples that only prove the point to someone who is already inclined to believe it. If your worldview is that Satan controls the world and the media, and is determined to bring the WTS down, you are willing to accept some very thin premises in order to maintain that point of view. Confirmation bias is a very powerful thing.