The wording is specific that the receptacle must be in or above _a_ countertop.
If you have a split level countertop, then the receptacle can be in the riser between the two. See this image from NFPA itself (this image is _not_ code, but indicates that at least someone at the NFPA holds this interpretation):
View attachment 2576378
So my question, relevant to the OP: just how large does the lower flat surface need to be to count and permit a receptacle in the riser between the two 'countertops'. IMHO you could have a place an outlet at the side of an island if it was shielded from below by a sufficient 'vestigial countertop' (possibly with some sort of raised rim) so that there are no dangling cords that a kid could grab or an adult could accidentally brush into; in other words, a 'vestigial countertop' that eliminates the risk presented by cords in the side of the island.