Why is this solution to the mountain ‘puzzle-in-a-puzzle’ incorrect

Both solutions are correct for this puzzle.

However, this puzzle controls the movement of the platform you're standing on. The first solution is for the side you were already on.

If you need to go back across to the other side, you will need to use the first solution.

The piece of paper gives you a solution that you can enter into the hexagon puzzle below the Windmill.

This is completely optional.