I have gone back and forth on this image, as to how coincidental it is. A key thing is that there are many people with cameras around, so the issue isn't how rare it is for a single person to get this shot - but for *someone* to get it - and that removes a big part of the coincidence caused by the fact, as mentioned earlier, that the shadow contrast is strong due to the camera being in the plane formed by the sun and *a particular* straight part of the plume. The camera isn't collinear with the plume, which would be much rarer - it is just coplanar with a particular section of the jagged plume, and that part casts a shadow with high contrast since you are looking through the volumetric slab of shadow. A regular crepuscular ray is visible in any orientation and doesn't have this high contrast effect due to coplanar alignment.
There are many images and videos on the web with strong shadows cast just like this during a rocket launch, and an important point is how dynamic they are - changing in contrast and even orientation slightly.
There is certainly a lot of wiggle room vertically in where the moon could be to still have this effect - and that is shown by the fact that the moon is actually a fair distance above the end of the shadow. But laterally, the moon is remarkably well centered on the shadow. If that is the real moon's disk - then it looks to be centered to within 5 arc-minutes or something - much, much less than the moon's potential distance from the ecliptic - which is around 5 degrees.
I checked TheSky for the moon's phase angle at that time, and it was around 5 degrees. That's not surprising that it would not be exactly full - but what did surprise me is that it's distance from the ecliptic was 2.5 degrees. That is very far from the true anti-solar point - which would be on the ecliptic and show huge misaligment from the shadow that would have weakened the impact of the image.
Another factor not mentioned is that neither the sun nor the moon is in the true location due to refraction. The shadow is cast by the refracted sun, which is around 1/2 degree off in a normal sunset, and presumably much farther off when viewed from high up where the plume casts the shadow - because the plume is looking through much more atmosphere than a normal sunset. The moon is also offset by many arc-minutes due to its low altitude. In addition, the volume of shadow being seen isn't at infinity - but is "up there" in the sky at some range of altitudes - allowing for some lateral range of orientation due to parallax. Viewers left and right of the shadow would still see good contrast, but the shadow would be slightly shifted.
A simple question is - are there any other pictures of this event, and how good is the moon alignment? I couldn't find other images by the original photographer, and he talks as if he just took the one picture and later realized he had captured a great atmospheric shot. Unfortunately this image and others like it are associated with mystical meanings - so it's hard to find good info on the web. But I did find one other image from a different location that captures much of the phenomena - and the moon is clearly misaligned:
http://www.thelivingmoon.com/47john_lea ... huttle.htm
The image is about halfway down the page.
One question is just how dynamic and long-lived the shadow was. Videos of plume shadows on youtube show the contrast to be fairly dynamic, and as long as the sun is setting and the moon rising, there will be some motion of the moon relative to the shadow. This makes me think this may have been snapped at the right moment to catch it exactly aligned, where all the factors cancel the offset of the moon's location from the ecliptic. The alignment of the shadow clearly isn't guaranteed to be so good based on astronomy alone, since the image I link above shows the moon quite a ways off in comparison. The APOD image may be one of many the photographer took, and the general scene persisted for some time - but he chose the one that had the best alignment. I certainly would have been shooting constantly in such a situation - even with film.
So - I think a lot of the general alignment is guaranteed by a near sunset launch with a full moon, but additionally the astronomical parameters conspired with refraction and the changing direction and refraction of the sun as it set to bring it even closer - and then the photographer chose the best aligned version from the dynamic scene he watched. It's not surprising that things are basically aligned - but the lateral alignment of the moon with the shadow is extremely good compared to what it might otherwise have been for a different lunar distance from the ecliptic.