Putnam and Kripke argue that from the direct reference theory of natural-kind terms stem "startling consequences for the theory of necessary truth", namely the existence of (non-trivial) examples of metaphysically necessary but conceptually contingent truths. I aim to show that the matter is not so plain, at least with regard to species-terms. To be precise, it is not possible to derive such consequences "merely" from the direct reference theory without presupposing a certain kind of essentialism (that I will call "genetic essentialism"). If this is correct, then not only is essentialism a premise rather then a consequence of Putnam's view. It is, moreover, a premise whose plausibility calls for empirical verification, and such a verification is far from being available.