You're talking about cosmonauts in earth orbit, not on the surface of the moon, and they say they can see just the brightest stars by looking away from the light source (Earth). Standing on the moon, the bright light source is taking up half of your field of view, and looking up puts the sun in your field of view.
The only way to easily see stars on the moon is either at night, or standing in a shadow to block the sun and looking up far enough to get the Moon's surface out of your field of view. And guess what? The Apollo astronauts said they could see stars when standing in the LM's shadow.