Instead of addressing your specific question, let's generalize, so that you might understand the larger picture. Is any dichotomy in language defensible? Yes and no. Sometimes. Maybe. Whether or not a definition is true depends on what you accept to be true of a definition. This is a perennial issue that rears its head in philosophical discussion because of the intimate relationship between epistemology and ontology. In the case of the natural and unnatural, it is both defensible to accept a binary category that accepts the principle of bivalence and to reject it in favor of fuzzy categories and multivalued logics. It's even possible to embrace the dialetheism.
On the one hand, it is very pragmatic to use the natural/unnatural, or natural/artificial (I think you intend the latter) distinction because it works, and yet, in the definitions, one might see the seeds of a contradiction born of the analytic meanings that inhere to the words. The preferences and methods of philosophy that are brought to bear on the question ultimately determine the answers philosophers reject, or accept as weak or even strong arguments.
Metaphysics or Philosophy of Language?
It may be tempting to go to metaphysics to answer this question, and some here shall, I have no doubt, to discuss the impact on ontological commitment required by the predicate natural. But I suggest linguistics and the philosophy of language on the basis of a naturalized epistemology. Hence, what philosophers know about language is much more decisive in answering this question than what philosophers think about the nature of 'natural'.
The Linguistic Turn and Words as Tools
Let's accept the findings of the linguistic turn. When you start talking about the nature of definition, you must first accept that definitions are to no small degree normative. That is to say, the general definition of natural and unnatural is a linguistic convention. No, people don't get together and vote on what words mean, but they do, in a way, cast a vote metaphorically by how they practice usage in their idiolect. If 99 out of 100 people use definition X, then from a descriptivist perspective, the definition is X regardless of its logical flaws. Is it possible that the general usage of natural and unnatural, therefore is logically inconsistent? You seem to offer a prima facie argument for that.
So, what does philosophy have to say about this? Well, that depends on your metaphysical presuppositions about language. Some philosophical dispositions lend themselves towards language prescription, where uses of definitions are compelled socially. A philosopher who believes in an absolutist notion of definition may try to argue that the definitions of natural and unnatural are correct not by virtue of their logical relationship, but perhaps because of the emancipatory politics of the governing body. For instance, in the USSR, lysenkoism is an instance of whether or not the truth of definitions and ideas is determined by political fiat. An instrumentalist view of language doesn't conceive definitions as right or wrong, so much as examines them for pragmatic outcome. That is, does the definition work for the people who use it?
Dissolving the Problem
So, now, we are in a position to answer questions about the natural, unnatural, and the supernatural.
The dichotomy between the natural and the artificial in general usage is absolutely defensible on the pragmatic grounds that it quickly seeks to establish two classes of things for the exchange of meaning. If you are in the infantry, what you want to know is 'is that thing you are about to step on natural or artificial. If it's artificial, like an anti-personnel mine, then you have to exercise extra caution. Even it's the wristwatch dropped by a hostile, it tells you something about the state of affairs that a natural object wouldn't. It tells you the enemy may be near, and that has survival value. Does the dichotomy perhaps fail to capture some of the finer grades of meaning about the relationship and origin of the materials of the thing? Absolutely! But are we more likely to survive if you stand around pondering the definition on a battlefield? Absolutely not. Hence, from an epistemic perspective, the definition is pragmatically true and the dichotomy is pragmatically defensible based on defeasible reasoning which strictly speaking may not be devoid of contradiction.
But let's now think about another context where a pragmatic definition might not suffice, where logical precision is much more important. Let's say you are defending an academic thesis, and the same question about whether an object on the table is natural or unnatural is posed, and it is important to answer to defend the thesis by impressing upon your advisor that you have a sophisticated use of language. In this case, the truth and utility of the definition might be a function of its epistemic coherence. Let's say you are explicitly called to undermine the dichotomy!
What if your thesis evaluator says asks you if sheep are natural because they have been subject to artificial selection. Said thesis evaluator accepts that sheep before Homo sapiens are natural, that robotic sheep by Boston Dynamics are unnatural, but then asks you to classify a sheep that has been bred over generations to be woolier is natural or unnatural? Is the atmosphere still nature because there are trace pollutants in it? Is any of earth still natural because of the widespread impact of human action on its biological, chemical, and physical composition? Here now definitions of what constitutes natural have a different role.
This is what is meant when talking about the normativity of truth and language. Whether or not a definition is true or a dichotomy holds depends on what you accept to be true of definitions and dichotomies. :D