Evolutionary relationships of the endemic South American ungulates (SANUs), both to each other and to other major placental clades, have been robustly debated for more than a century. Morphological evidence has not provided unambiguous resolution of these controversies, although recent paleoproteomic and paleogenomic analyses have supplied unequivocal evidence that at least Litopterna and Notoungulata are most closely related to each other and then to crown Perissodactyla. A recent study based on morphological characters has gone much further, claiming that litopterns and South American condylarths are stem to, or even nested within, Perissodactyla, but are not otherwise related to any North American clades of archaic ungulates. This study also concluded that the alleged shared presence of perissodactyls in Paleogene South America and India, along with several other biological groups, is evidence of a fluid biotic interchange early in the Cenozoic. Our assessment of this study revealed various conceptual and methodological errors, including misinterpretation of homologies, scoring errors, and failure to include relevant taxa such as Notoungulata. Our corrected phylogenetic analysis, performed with essentially the same taxon/character sampling and searching options, recovered all litopterns and their relatives in a single monophyletic clade, separate from the one representing Perissodactyla s.s. Both clades are clearly derived from Laurasian ungulate ancestors. In addition to the absence of true perissodactyls in Paleogene South America, most of the biological groups postulated as shared by both continents are not found in Paleogene strata of India. In sum, there is no meaningful evidence supporting the alleged multiclade, multiterrain biotic interchange.