Edward, in no historical record, especially in interviews and items designed for general consumption, will there ever be perfect consistency.
The fact is that Apollo astronauts have noted that they could see stars with ease when in the umbra of the Moon, and with some difficulty (due to sunlight reflecting off the docked LM, or directly in through windows) during translunar and trans-Earth coast.
It is also a fact that the crews could generally not see stars from their suits on the lunar surface, due to the difficulty in avoiding all reflected sunlight. Armstrong and Aldrin certainly didn't have time to try it on their trip to the Moon, although they could see stars through the LM's optics (which could avoid stray sunlight).
Also, one of the crewmen on the later missions - Edward Mitchell? - someone will correct me - did go to the trouble of finding a large shadow to lurk in, and managed to block off enough light to view the stars directly. But in fact, the stars even at lunar night are not overwhelmingly better than from a good dark-sky site on Earth; our atmosphere attenuates only about 15% (IIRC) of the visible.
I hope that resolves your issue.
Edit to add: I went back and re-read your message. Simply put, the stars would be equally visible, or not visible, from an airless Earth, depending on the lighting conditions. With no atmosphere at noon, you'd have the same challenges of avoiding stray sunlight. The APOD picture doesn't change this; it's just a picture for popularization of science.
