But I could ask an a similar sequence of questions in response to whatever interpretation you might propose.

Agreed. But I asked those questions not because I think your reasoning was inherently wrong, but because I felt like you were making a post-hoc story to justify specifically the answer A. While some sort of problem-solving logic that happens to generate A provides fairly easy answers for those kinds of questions, generating A post-hoc does not help answer them.

I don't think "it's probably supposed to be a test of physical intuition" is all that plausible

Why not?

It would be a pretty bad test of physical intuition of the sort you describe, but a pretty good test of spatial reasoning, and I assume that the army people are competent at designing tests. If it was a test of physical intuition, why change how the objects were attached to each other in each answer? And so on and so forth.

Note: If you asked me "why would they change the relative positions in each answer if it was a test of assembling objects?" I would say "Because changing things around increases the need for spatial reasoning."

Your link doesn't specifically support that.

I thought the evidence was strong enough to say that pretty confidently, but you're right it's not overwhelming.

Additional note: if you look at the page Unnamed linked to, you'll see that the picture is all one piece, and the instructions are down below in text. If the question we got this picture from was similar, that may explain the disappearing instructions!