This is what de Candolle had to say about artificial classifications:
"Others have as their essential goal to give to persons who know nothing of the names of plants an easy way to discover the names in the books by inspection of the plant itself. These classifications have been given the name of Artificial Methods."And,
"...there are those persons who want to study plants, either in themselves, or in their real relations among themselves, and to class them so that those plants most closely related in the order of nature are also those most closely related in our books. These classifications have received the name of Natural Methods."De Candolle considers Systems and Methods.
A system is a key or classification based on a particular organ - leaf, flower, etc.
A method is a key or classification based on all of the organs of a plant; methods are sub-divided into artificial and natural depending on their purpose.
De Candolle again:
"classes that are truly natural, established on the basis of one of the major functions, are necessarily the same as those established on the basis of the other."That is, congruence.
Bar-coding, based on "a particular organ", interpreted as a piece of DNA, is, in this sense, a system. It might be seen as an artificial classification as its purpose is to find the name of any given plant or animal.
Now, is molecular systematics a system or a method? It too is based upon "a particular organ", so it too might be considered a system. Now if considered a method, we see that there is no notion of congruence at all as no other datasets are given consideration. Molecular systematics as a form of measuring similarity constitutes a system, not a method.
Ancestors and other mechanical explanations are not of any concern in the debate between artificial and natural classifications. One does not decide on homology in advance. It is either there or it is not. Homology, as we understand, is a relation. A similarity such as 11, or AA, is not a relation. Thus, all molecular systematic studies are phenetic as they ignore relationship, that is, homology.