This study offers a rigorous meta-critical appraisal of the controversial historical claims surrounding the Archive of the Dukes of Medina Sidonia in Spain, which allegedly contain documents pointing to pre-Columbian Andalusian and Moroccan contacts with the American continent. Operating under the methodological constraint of restricted direct access to the physical documents, the paper shifts the analytical focus toward the epistemic status of exceptional historical claims. Through a composite multi-disciplinary framework, the study systematically synthesises the institutional history and access policies of the archive, evaluates the strategic and technical limits of medieval Islamic Atlantic seafaring, and reviews the comprehensive absence of independently verified archaeological or genetic evidence of a pre-1492 Islamic presence in the New World. Key historical contentions such as the alleged transoceanic voyage of Yāsīn, 9th-century Andalusian trade networks, and the strategic deployment of Arabic interpreters by Columbus are rigorously contextualised and evaluated against established historical and scientific consensus. Moving beyond binary acceptance or outright rejection, the study invokes the classic Latin formulation non liquet ("it is not clear"), advocating for a stance of methodological suspension. It concludes with a revised research agenda, proposing alternative archival strategies and empirical criteria required to transform unverified archival claims into established historical facts. This paper is essential reading for scholars interested in historical criticism, maritime history, archival studies, and the epistemology of global geographical discoveries.