Well, as I said in the "Spock wearing wrong shirt" thread, I've always thought it possible that Spock had a "double major" while at the Academy -- both Science and Command.One must also assume that the curriculum at SA evolved over time. Spock may have never taken the test either because he never attended command school (he was a blue tunic, and didn't take over as XO until after Gary Mitchell perished) or because the KM test didn't exist back then.
At some point, someone came up with the notion of presenting command school cadets with a no-win simulation to measure how they would react in the face of a situation that couldn't be resolved in a survivable manner no matter what action was taken. Old school officers Like Pike and April probably never took the test either.
I don't recall the KM scenario ever being mentioned in TNG. It's possible that the test was later dropped for one reason or another. Policies and leadership change over time, and the curriculum continues to evolve.
Being who he is, he preferred science (hence the blue shirt) but he was obviously qualified for command (as seen in many TOS episodes), and was perhaps trained in both.