Is there any way to set up a classroom (or an educational system) so that these students would get the right answer? Alternatively, is it even desirable?

If you teach students to think this way, you're saying "The world is governed by comprehensible scientific laws -- which is irrelevant, because people are constantly screwing with you." This experiment might be useful in a physics class for lawyers (who would probably catch on) or conspiracy theorists (who would, at least, have more entertaining hypotheses).

A compromise might be for the teacher to not just ask for an explanation, but ask for a testable explanation, and reward people for coming up with a theory they can falsify. The sad truth is that there's one more group that would figure out the answer right away: Creationists.