I truly believe it is just as the opening post suggests: a GB member starts saying how "they" feel that their helper is anointed and has great responsibility ahead of himself, so he starts partaking.
I believe that each GB member has, somewhere along the way, anguished over whether he is actually anointed or if it's all bullshit. I can tell you that I was a full-believing JW and I can only relate it to being appointed an elder.
I never worried about attaining the title and actually liked it when I wasn't an elder. But I thought holy spirit was working through the elders and when they came to ask me to accept the assignment, I assumed it was Jehovah working through others. I went through that "Is it all bullshit" period, but not until much after my appointment. I gotta think it's much the same for "anointed."