In this case, isn't this just a matter of the definition of a "heap of sand"? The article seems to sort of forget to define a heap and just proceeds to make a problem out of it and asking questions like "when does a heap become not a heap?" when it was never even defined why would we call something a heap in the first place.
So I think the real question there is just that why are you calling something a heap in the first place and when you have an answer to that, that same answer will also help you with figuring out when the thing you call a heap is not a heap anymore.