That whole "You wouldn't want to bring reproach on Jehovah's name, would you?" line is becoming more and more obvious as nothing more than a convenient ploy used by elders to keep things secret.
I often think of the David and Bathsheba affair, which resulted in many bad things, including death, but did Jehovah try to hide the scandal to protect his name? No. Instead he had it put in the Bible (so JWs believe) for all to read.
What Jehovah's Witnesses are really trying to protect with such a remark is their own reputation and public image, which is becoming more tarnished all the time.