The saying can be seen as mystifying the abilities of stronger players. But I think there are also more charitable readings. I think the second and third stage in the saying might refer to the same as the “rigorous” stage and the “post-rigorous” stage in this article. Instead of saying that in the third stage on sees "just stones again" (I might have replicated that part badly), it might be more correct that one can see the stones again, because the formalisms aren't in your way anymore.

I prefer this sentiment. "Deep" nonsense saying things are all the same when they aren't doesn't belong in a rationality tract.

Well, I assume it was included mostly for poetic reasons. Which is not an excuse, of course.