Why, if these 'double shadows' are caused by multiple light sources, are they parallel? Shadows caused by multiple light sources diverge and at angle equal to the angle between the light sources at the vertex (source) of the shadow.
Yes, this is a rather important question. "Two apparent shadows means two light sources" is not enough when we know rigorously the geometry that would have to exist between those shadow volumes. If the observed light-and-dark patches purported to be overlapping shadows don't exhibit the right geometrical properties for such a scenario, that is data that argues against that hypothesis. We'd have to look at other hypotheses and obtain data to test them.
One that's improbable in this scenario but which comes up frequently in other forms of photographic interpretation is coloration of the surface. I can shoot a photograph of a flat wall on which is painted a representation of some scene or object. If care is taken to color the wall so as to resemble shade and shadow, the illusion of depth is produced. This is, in fact, how a great deal of scenery art is accomplished in film and theatre. We always keep this on the table because such
trompe l'oeil circumstances arise accidentally often enough in nature. The coloration of unfamiliar or previously unknown objects gives us bad spatial cues. Not likely to be the case here because we can deduce the absence of any rampant, hard-edged coloration variance on the lunar surface, and because of the complexity of the contour in the feature.
And of course there's the interreflection hypothesis. It answers the contour question as well as aligning with when we know the astronauts photographed through double-paned glass versus when they didn't. It's a very parsimonious explanation. "But it doesn't occur all the time," is not much of a response. Yes, we can show through demonstration that it doesn't occur all the time. And with a little systematic experimentation we can enumerate some general factors that affect whether we see it any particular case or not. That rarely lets us declare whether it should be visible or not in any imagined case. But it convinces us that its comings and goings are governed by conditions, not by the whim of the observer.
That it wasn't duplicated exactly in some particular test setup is not worrisome. As we've noted, there are many factors involved. Even in the most charitable cases, we don't afford much to a claimant's failure to demonstrate or reproduce a hypothesis that competes with his own. It's a conflict of interest, even if there's no nefarious intent. But the claimant's inability or unwillingness to apply empirical tests to his own hypothesis speaks louder. You win your case by showing empirically that your hypothesis works, not by a show of failure to empirically verify your critics' counterproposal.