This is all very strange to me. My volunteer parish choir of about twenty people all read music, standard and Gregorian. Everyone sight-reads at least tolerably well, too. I can’t imagine how you could regularly learn new pieces otherwise, at least without having to rehearse them over and over, or bring in a stereo for people to listen to.
I wonder, though. For those people who are competent choral singers but say they “don’t read music,” do they just mean that they can’t sight-read and can’t hear a piece in their head by looking at the notes? They must have some idea of what those little round things on those lines over the words are, right? When they move upward, the pitch goes up; when they jump downward, the pitch jumps down; when the “alligator mouth” opens toward the right, you get louder; and so on? It’s not like what happens when I look at, say, Thai or Arabic script, which I only see as completely indecipherable squiggles, is it?