This isn't an urban legend, but I think it ties in because you can see how a reputation and public persona were cultivated.
When I was studying, the brother who was teaching me was talking about the anointed, and particularly the governing body, telling me about how close to God they were, how they knew the bible so intimately through and through. He told me of having seen one of them at a district convention (I don't remember which GB member it was) get up and deliver a long talk, using numerous references to bible scriptures where the audience looked them up and read along as he spoke the words aloud. After this talk, the chairman came forward, handed him a paper with some statistics regarding attendance and so forth, and asked him to read them to the audience. The GB member responded that he was unable to read because he had come up onstage without his glasses.
Well, I was suitably impressed with his ability to deliver the entire talk, including quoting scriptures verbatim, without reading anything.
Cut to a few years later, district convention where I am in attendance: a GB member gives a long talk, citing numerous scriptures which we look up and follow as he quotes them. Afterward, the chairman comes up onstage. He does not take the podium from this brother, but is holding a microphone in his hand and speaks beside the GB; this allows the audience to hear the GB's words. He states that he has the statistics regarding the attendance, blah blah blah...
At this point, I thought to myself, "Oh, my goodness, no..."
The chairman asks the GB to read the statistics. I think, "Oh, no, don't do this, please."
The GB tells the chairman that he can't read the paper. The chairman feigns confusion: "What... you can't read it... I don't..." The GB tells him, "No, you see, I left my glasses behind when I came up onstage."
My heart just sunk. I was stunned, sitting there knowing that they had deliberately contrived this scene, and knowing that the purpose of it was to make the GB guy look oh-so-holy-and-wise.
So the chairman hams it up a little bit. He's got to repeat it for everybody, so they'll be sure and get the point, that this guy just delivered that talk without reading anything: "you forgot to bring your glasses, Br. GB?" Exaggerated pronunciation, dragging the words out, staring at the audience with mouth hanging wide open, showing us how awestruck we all should be.
That's the only thing I can remember from that assembly: how they were trying to create a persona by staging that incident, one that they had used in the past as well.