When entering the game starting by selecting difficulty it uses the previous game even if no moves have been taken. See this video I made for an example. I think hard resets should be required to stop players potentially knowing the solution beforehand. Perhaps there are other games that do something similar but I haven't looked too closely yet.

Should players be asked to switch difficulty at the beginning of the video to get an authentic run?

In the video it doesn't reset even after switching difficulties (from easy to medium and back to easy). I think there has to be other visual confirmation, like selecting "start a new puzzle".