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AI evaluation is increasingly central to AI safety and governance, yet taking part in an evaluation does not by itself confer authority over its design, its execution or the resources it depends on. This paper examines how infrastructure arrangements distribute that authority, and so shape who can evaluate AI systems independently. Drawing on Science and Technology Studies, political economy and applied evaluation standards, we introduce PAAI (Power, Access, Adequacy, Independence), a framework for examining who controls evaluation infrastructure, the terms on which it is available, whether it is adequate to the evaluation's purpose and what autonomy it supports. We apply PAAI to twelve African AI evaluation projects (2022-2025) and to the documented roles of all ten member institutes in the three published joint testing exercises of the international network of AI Safety Institutes. We identify three recurring configurations: extractive collaboration, dependent innovation and constrained independence. African actors often contribute data, language expertise and task design while external institutions retain authority over infrastructure and evaluation frameworks; design authority without infrastructure authority never yielded more than partial independence. The joint testing exercises show a similar division among mostly high-income members: the institutes that led each exercise also ran the models, while Kenya, the network's only African member, moved from annotation to task design with no documented model execution. Participation in evaluation does not by itself produce evaluative authority. For evaluation to serve as a credible governance mechanism, access must come with control over priorities, methods, publication and continuity.