A recent paper in this journal has challenged the idea that complex adaptive features of proteins can be explained by known molecular, genetic, and evolutionary mechanisms. It is shown here that the conclusions of this prior work are an artifact of unwarranted biological assumptions, inappropriate mathematical modeling, and faulty logic. Numerous simple pathways exist by which adaptive multi-residue functions can evolve on time scales of a million years (or much less) in populations of only moderate size. Thus, the classical evolutionary trajectory of descent with modification is adequate to explain the diversification of protein functions.