Recently, many phylogenies of a diverse array of taxa have been published that are solely based on DNA-sequence data. Typically, these “new” phylogenies are compared to previously established classifications that were not necessarily based on the same rigorous methodologies of current phylogenetic systematics. This comparison often details the support that the “new” phylogenies give to previous classifications without added insight into how such molecular studies can improve prior classifications. Using a recently published molecular phylogeny of robber flies (Diptera: Asilidae) as an example, it is shown that this common line of argumentation is unsound for two main reasons. First, the sheer comparison does not entail a scientific test because morphological features used as the basis for the previous classifications are not incorporated into the molecular analysis and, therefore, the morphological characters remain as yet-to-be-tested hypotheses of homology. Second, earlier classifications may be based only on a few diagnostic features without character assessment in the Hennigian sense, and accompanying published diagrams of relationships therefore are not cladograms in a strict sense. Mere comparison of a molecular phylogenetic hypothesis with a classification based on overall similarity is not theoretically sound. Interpretation should go beyond this point to understand how previous classifications and diagrams of relationships were obtained, and what information they hold that can simultaneously test molecular characters. Rather than simply discussing similarities and differences to past classifications, modern phylogenetic studies should improve previous hypotheses by applying (1) many character complexes; (2) broad taxon sampling; and (3) simultaneous phylogenetic methods.