Startups Giving Problems to Solve That They Didn't Solve?

I recently had a programming problem concerning a Rubik's cube as a challenge problem to get a job with them.

The problem was given any color configuration or rotation of a cube, be able to find a canonical form to "look up" a solution.

In their minds, you should be able to rotate any cube (24 possible states), and then permute the colors (6! = 720 possible ways to rearrange WYGBRO), and yet, this is entirely wrong from my understanding.

In a follow up meeting, they showed me an example case where instead of using the colors WYROGB, they used the number 0-5 instead, and then claimed this was valid. But they don't realize that they are breaking their own constraints given in the problem.

Is there anyway to prove them wrong? I asked to sign an NDA because I'm genuinely just curious about how to better my understanding if I am wrong, but I'm getting the feeling they are intentionally not wanting to admit they are wrong.

Is there any thing I can do to actually get a response that shows how I am wrong or seek remedy ?