Following the set of informal proposals by Wright and Gillman (2022) to modify the International Code of Nomenclature for algae, fungi, and plants (ICN, the Code: Turland et al., 2018), in which the authors demanded to allow the retroactive replacement of well-established, valid and legitimate scientific names of organisms with some “indigenous” names, meaning supposedly “pre-existing” vernacular names used by Indigenous Peoples, I presented my detailed counterarguments (Mosyakin, 2022/2023). I advocated for the stability of biological nomenclature, protested against its possible large-scale disruption, and concluded that any “attempts or proposals aimed at granting preferences in biological nomenclature to any political, racial, ethnic, social, gender, religious or other group or groups should be rejected as discriminatory acts”. In response to my criticism, Wright and Gillman (2023) tried to address and debunk some of my arguments. They denied the potentially discriminatory nature of their proposals, insisted on their ideas of using “indigenous” names for replacing retroactively at least some well-established scientific names of organisms, but at the same time modified some of their earlier claims. Unfortunately, these modifications also fail to fit the principles and rules of the current Code, and even those of any other rationally built code of biological nomenclature. In particular, the earlier proposals by Wright and Gillman (2022) on author citations and authorship clearly contradict their new ideas. They now propose to ascribe the authorship of the nomenclaturally new “indigenous” replacement names to the authors of the replaced names, and at the same time they think that those authors are not the authors of names but the authors of “descriptions”. I analyze here these and some other misunderstandings and misinterpretations of the Code. I also demonstrate and confirm, with proper references to relevant sources, the potentially discriminatory nature of any nomenclatural proposals aimed at providing the exceptional or preferential rights to any groups of authors and/or users of biological nomenclature on the basis of their racial, national, ethnic, or ethnocultural identity. I conclude that the “modified” proposals of Wright and Gillman (2023), still aimed at possible replacement of established valid and legitimate scientific names with some vernacular, folk, legendary, fabulous, or traditional (including “indigenous”) names based on the supposed “chronological priority” going before the starting date of 1753, are disruptive for biological nomenclature, illogical or naïve, and simply non-implementable in practice. I briefly consider here some rational and acceptable alternatives for addressing the issues of non-discrimination, real equity, diversity, representation, and recognition of traditional knowledge in biological nomenclature, including several formal proposals to amend the Code, to be considered at the Nomenclature Section of the XX International Botanical Congress (July 2024, Madrid, Spain).