Guest Bob,
Your dance caller rules seem to sum it up pretty well for me. I'd adapt them as follows:
1. DO learn your song and rehearse it so you won't have to read it from a book or notes.
(Exception: In some settings you may get requests for songs you didn't specifically rehearse to perform that night, in which case making using your own notebook of songs may not be such a bad thing.)
2. Even if you've performed a song hundreds of times without notes, if it's important to get the lyrics right and it's not a simple, short song, it can be helpful to have some sort of lyric sheet or "cue card" where you can glance at it unobtrusively.

Jim C, you can't maintain eye contact with anyone continuously (that's called staring) -- especially with a whole audience.   Your eyes glance around the room as you're looking at the audience, and a quick glance at a page of music can be hardly more noticeable than blinking.
I just think it's intolerant to dismiss a performer just because there's a music stand or such in front of him/her, even if they obviously know the song and are not just using the song sheet as a substitute for rehearsal.
The analogy to speakers using teleprompters is valid insofar as professionals can often use large-print cue cards or teleprompters without the audience being able to tell that they are using them.