Yes, this is true! But for our learning purposes, the sentence still translates to "You don't see a duck but a bird." Scientific classification is probably beyond the scope of the course... although i think I remember a sentence or two about ducks, hens and geese being birds... :-)
Maybe the question might be, is there any way in Czech that this sounds okay? Does the word ptáka somehow in practical use seem like it is non-duck birds? If it sounds just as silly in Czech than it does in English, we know that the word "bird" is indeed an exact translation in every scenario.